254 + Interview Questions in SYSTEM-OF-PARTICLES IN GENERAL AWARENESS Page 4 InterviewSolution

151.	A disc of mass `m` and radius `r` placed on a routh horizontal surface. A cue of mass `m` hits the disc at a height `h` from the axis passing through centre and parallel to the surface. The disc will start pure rolling for.A. `hltr/3`B. `h=r/2`C. `hgtr/2`D. `hger/2`
Answer» Correct Answer - B Linear momentum is conserved, `mv=mv`. Angular momentum abouty centre of the disc. `=mvh=-Iomega=(mr^(2))/2 omega` or `omega=(2vh)/(r^(2))` For pure rolling `v=r omega=(2vh)/r` or `h=r//2`, for pure rolling.

Discussion

152.	Moment of inertia of a hoop suspended from a peg about the peg isA. `MR^(2)`B. `(MR^(2))/2`C. `2MR^(2)`D. `(3MR^(2))/2`
Answer» Correct Answer - C It is equivalent to ring rotating about an axis passing through tangent.

Discussion

153.	A hoop of mass `500gm` & radius `10cm` is placed on a nail, then the moment of inertia of the hoop, when it is rotated about the nail will be ____`kgm^2`A. `0.05`B. `0.02`C. `0.01`D. `0.03`
Answer» Correct Answer - C `I=mr^(2)+mr^(2)=2mr^(2)`

Discussion

154.	The moment of inertia of a wheel of radius `20 cm` is `40 kgm^(2)` if a tangential force of `80 N` applied on the wheel, its rotational `K.E.` after `4s` isA. `16.2J`B. `51.2J`C. `25.6 J`D. `24.8J`
Answer» Correct Answer - B `omega=omega_(0)+alphat, KE=1/2Iomega^(2)`

Discussion

155.	A wheel has a speed of `1200` revolution per minute and is made to slow down at a rate of `4 rad//s^(2)`. The number of revolutions it makes before coming to rest isA. `143`B. `272`C. `314`D. `722`
Answer» Correct Answer - C `omega=(2piN)/(2t)` and `theta=(omega_(1)^(2)-omega_(1)^(2))/(2alpha)`

Discussion

156.	A fly wheel of `M.I. 6xx10^(-2) kgm^(2)` is rotating with an angular velocity of `20 rad s^(-1)`. The torque required to bring it to rest in `4s` isA. `1.6 Nm`B. `0.6 Nm`C. `0.8 Nm`D. `0.3 Nm`
Answer» Correct Answer - D `tau=Ialpha`

Discussion

157.	A wheel rotating with uniform angular acceleration covers 50 revolutions in the first five seconds after the start. Find the angular acceleration and the angular velocity at the end of five seconds.A. `4 pi rad//s^(2),80 pi rad//s`B. `8 pi rad//s^(2),40 pi rad//s`C. `6pi rad//s^(2),40 pi rad//s`D. `6pi rad//s^(2),80 pi rad//s`
Answer» Correct Answer - B `theta=2piN,theta=omega_(0)t+1/2alphat^(2)`

Discussion

158.	A gymnast standing on a rotating stool with his arms outstretched, suddenly lowers his armsA. his angular velocity decreasesB. his angular velocity increasesC. his moment of inertia remains sameD. his moment of inertia increases
Answer» Correct Answer - B

Discussion

159.	The area of the triangle whose adjacent sides are represented by the vector `(4hat i + 3 hat j + 4 hat k)` and `5hat i` in sq. units isA. `25`B. `12.5`C. `50`D. `45`
Answer» Correct Answer - B Area of triangle `=1/2\|vec(A)xxvec(B)\|`

Discussion

160.	The are of the parallelogram whose adjacent sides are `P=3hat i + 4 hat j, Q = -5 hat i + 7hat j` is (in sq. units)A. `20.5`B. `82`C. `41`D. `46`
Answer» Correct Answer - C Area of parallelogram `=\|vec(P)xxvec(Q)\|`

Discussion

161.	The angular velocity of a rotating body is `vec omega = 4 hat i + hat j - 2 hat k`. The linear velocity of the body whose position vector `2hati + 3 hat j - 3 hat k` isA. `5 hati+8 hatk+14 hatk`B. `3hati+8hatj+10 hatk`C. `8hati-3hatj+2 hatk`D. `-8hati+3hatj+2hatk`
Answer» Correct Answer - B `vec(v)=vec(omega)xxvec(r)`

Discussion

162.	The unit vector perpendicular to `vec A = 2 hat i + 3 hat j + hat k` and ` vec B = hat i - hat j + hat k` isA. `(4hati-hatj-5hatk)/(sqrt(42))`B. `(4hati-hatj+5hatk)/(sqrt(42))`C. `(4hati+hatj+5hatk)/(sqrt(42))`D. `(4hati+hatj-5hatk)/(sqrt(42))`
Answer» Correct Answer - A `hat(n)=(vec(A)xxvec(B))/(\|vec(A)xxvec(B)\|)`

Discussion

163.	The position of a particle is given by `vec r = hat i + 2hat j - hat k` and its momentum is `vec p = 3 hat i + 4 hat j - 2 hat k`. The angular momentum is perpendicular toA. `x`-axisB. `y`-axisC. `z-`axisD. line at equal angles to all the axes
Answer» Correct Answer - A `vec(r)xxvec(F)=vec(tau), vec(tau)botx-`axis

Discussion

164.	The linear and angular velocities of a body in rotatory motion are `3 ms^(-1)` and `6 rad//s` respectively. If the linear acceleration is `6 m//s^2` then its angular acceleration in `rad s^(-2)` isA. `6`B. `10`C. `12`D. `2`
Answer» Correct Answer - C `(alpha)/a=(omega)/v`

Discussion

165.	At a given instant of time the position vector of a particle moving in a circle with a velocity `3hat i - 4 hat j + 5 hat k` is `hat i + 9 hat j - 8 hat k`. Its angular velocity at that time is:A. `((13 hati-29hatj-31hatk))/(sqrt(146))`B. `((13 hati-29 hatj-31hatk))/146`C. `((13 hati+29 hatj-31hatk))/(sqrt(146))`D. `((13 hati+29hatj+31hatk))/146`
Answer» Correct Answer - B `vec(omega)=(vec(r)xxvec(v))/(r^(2))` `3hati-4hatj+5hatk=(xhati+yhatj+zhatk)xx(hati+9hatj-8hatk)`

Discussion

166.	Two point P and Q. diametrically opposite on a disc of radius R have linear velocities v and 2v as shown in figure. Find the angular speed of the disc.A. `v/R`B. `(2v)/R`C. `v/(2R)`D. `v/(4R)`
Answer» Correct Answer - C `omega=v/x=(2v)/(x+2R), rArrx=2R, omega=v/(2R)`

Discussion

167.	A particle of mass `m` is moving in a plane along a circular path of radius `r`. Its angular momentum about the axis of rotation is `L`. The centripetal force acting on the particle is.A. `(L^(2))/(mr)`B. `(L^(2)m)/r`C. `(L^(2))/(mr^(2))`D. `(L^(2))/(mr^(2))`
Answer» Correct Answer - D `L=mvrrArrv=L/(mr)` centripetal force `F=(mv^(2))/r=(L^(2))/(mr^(3))`

Discussion

168.	Four particles each of mass `m` are placed at the corners of a square of side length `l`. The radius of gyration of the system about an axis perpendicular to the plane of square and passing through its centre isA. `l/(sqrt(2))`B. `l/2`C. `l`D. `sqrt(2)l`
Answer» Correct Answer - A `I=Sigmamr^(2)=4m[l/(sqrt(2))]^(2)=(4ml^(2))/2=2ml^(2)` Radius of gyration `k=sqrt(l/M)=sqrt((2ml^(2))/(4m))=l/(sqrt(2))`

Discussion

169.	Four particles each of mass `m` are placed at the corners of a square of side length `l`. The radius of gyration of the system the moment of inertia of four bodies about an axis perpendicular to the plane of frame and passing through a corner isA. `ML^(2)`B. `2ML^(2)`C. `2sqrt(2)ML^(2)`D. `4ML^(2)`
Answer» Correct Answer - D `I=2[ML^(2)]+M[Lsqrt(2)]^(2),=2ML^(2)+2ML^(2)=4ML^(2)`

Discussion

170.	A uniform box is kept on a rough inclined plane. It begins to topple when `theta` is equal to: A. `30^(@)`B. `60^(@)`C. `tan^(-1)(1/2)`D. `45^(@)`
Answer» Correct Answer - C `mg sin thetaxxx=mg cos thetaxxx/2` taking moment about right bottom corner `rArrtan theta=1/2`

Discussion

171.	A square is made by joining four rods each of mass `M` and length `L`. Its moment of inertia about an axis PQ, in its plane and passing through one one of its corner isA. `6ML^(2)`B. `4/3 ML^(2)`C. `8/3 ML^(2)`D. `10/3 ML^(2)+`
Answer» Correct Answer - C `M.I.` about an axis passing through the diagonal `I_(g)=(2ML^(2))/3 M.I.` about the given axis `I=I_(g)+4M(L/(sqrt(2)))^(2)`

Discussion

172.	The moment of inertia of `HCl` molecule about an axis passing through its centre of mass and perpendicular to the line joining the `H^+` and `Cl^-` ions will be (if the inter atomic distance is `1A^@`)
Answer» `r=1Å=10^(-10)m , m_(1)=1 am u, m_(2)=35.5 am u` Reduced mass `mu=(m_(1)m_(2))/(m_(1)+m_(2))=0.976 am u` `~= 1.624xx10^(-27)kg [ :. 1 am u=1.67xx10^(-27) kg]` Moment of inertia about an axis passing through centre of mass of two particle system and perpendicular to the line joining them is `I=mur^(2)=1.624xx10^(-47) kg m^(2)`

Discussion

173.	Moment of inertia of body depends uponA. distribution of mass of the bodyB. position of axis of rotationC. temperature of the bodyD. all of the above
Answer» Correct Answer - D

Discussion

174.	Of the two eggs which have identical sizes, shapes and weights, one is raw and other is half boiled. The ratio between the moment of inertia of the raw to the half boiled egg about central axis is:A. `=1`B. `gt1`C. `lt1`D. not comparable
Answer» Correct Answer - B

Discussion

175.	A uniform cylinder has radius `R` and length `L`. If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular face is `mg` equal to the moment of inertia of the same cylinder about an axis passing through its centre and normal to its length, then
Answer» Moment of inertia of cylinder about an axis passing through centre and normal circular face `=(MR^(2))/2` Moment of inertia of cylinder about an axis passing through centre and its length `=M[(L^(2))/12+(R^(2))/4]` But `(MR^(2))/2=M[(L^(2))/12+(R^(2))/4]` `(R^(2))/2=(L^(2))/12+(R^(2))/4rArr(R^(4))/4=(L^(2))/12,` `:. L=sqrt(3)R`

Discussion

176.	A uniform cylinder has radius `R` and length `L`. If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular face is `(mR^(2))/2` is equal to moment of inertia of the same cylinder about an axis passing through its centre and normal to its length, thenA. `1:sqrt(2)`B. `1:2`C. `1:sqrt(3)`D. `1:3`
Answer» Correct Answer - C `(MR^(2))/2=(ML^(2))/12+(MR^(2))/4`

Discussion

177.	The moment of inertia of a solid cylinder about its natural axis is `I`. If its moment of inertia about an axis `bot^r` to natural axis of cylinder and passing through one end of cylinder is `191//6` then the ratio of radius of cylinder and its length isA. `1:2`B. `1:3`C. `1:4`D. `2:3`
Answer» Correct Answer - A `I=(MR^(2))/2,I_(1)=(19I)/6=(ML^(2))+(MR^(2))/4`

Discussion

178.	Two identical circular plates each of mass `0.1 kg` and radius `10cm` are joined side by side as shown in figure. Their moment of inertia about an axis passing through their common tangent is A. `1.25xx10^(-3) kg m^(2)`B. `2.5xx10^(-3) kg m^(2)`C. `1.25 xx10^(-2) kgm^(2)`D. `2.5xx10^(-2) kg m^(2)`
Answer» Correct Answer - B `I=2I_(1) & I_(1)=5/4 MR^(2)`

Discussion

179.	Two identical circular plates each of mass `M` and radius `R` are attached to each other with their planes `bot^r` to each other. The moment of inertia of system about an axis passing through their centres and the point of contact isA. `(MR^(2))/4`B. `(5MR^(2))/4`C. `3/4 MR^(2)`D. `MR^(2)`
Answer» Correct Answer - C `I_(1)=(MR^(2))/2+(MR^(2))/4=3/2MR^(2)`

Discussion

180.	Two circular rings each of mass `M` and radius `R` are attached to each other at their rims and their planes perpendicular to each other as shown in figure. The moment of inertia of the system about a diameter of one of the rings and passing through the point of contanct is A. `3/2 MR^(2)`B. `3/4MR^(2)`C. `5/2MR^(2)`D. `5/4MR^(2)`
Answer» Correct Answer - C `I=2MR^(2)+(MR^(2))/2=(5MR^(2))/2`

Discussion

181.	A thin wire of length L and uniform linear mass density `rho` is bent into a circular loop with centre at O as shown. The moment of inertia of the loop about the axis XX is`
Answer» `I=3/2MR^(2)=3/2xxlrhoxx(1/(2pi))^(2)=(3rhol^(3))/(8pi^(2))`

Discussion

182.	A thin rod of length `L` of mass `M` is bent at the middle point `O` at an angle of `60^@`. The moment of inertia of the rod about an axis passing through `O` and perpendicular to the plane of the rod will be A. `(ML^(2))/6`B. `(ML^(2))/12`C. `(ML^(2))/24`D. `(ML^(2))/3`
Answer» Correct Answer - B Moment of inertia of a uniform about one end `=(mL^(2))/3 :.` moment of inertia of the system `=2xxm/2((L//2)^(2))/3=(mL^(2))/12`

Discussion

183.	`I` is moment of inertia of a thin circular plate about its natural axis. The moment of inertia of a circular ring whose mass is half of mass of plate but radius is twice the radius of plate about an axis passing through any tangent of ring in its plane isA. `3I`B. `4I`C. `6I`D. `1.5 I`
Answer» Correct Answer - C `I=(MR^(2))/2, I_(1)=3/2M_(1)R_(1)^(2)=3/2[M/2][2R]^(2)=6I`

Discussion

184.	A thin rod of mass `M` and length `L` is bent into a circular ring. The expression for moment of inertia of ring about an axis passing through its diameter isA. `(ML^(2))/(2pi^(2))`B. `(ML^(2))/(4 pi^(2))`C. `(ML^(2))/(8pi^(2))`D. `(ML^(2))/(pi^(2))`
Answer» Correct Answer - C `I=(MR^(2))/2` but `2piR=LrArrR=L/(2pi)` `:. I=(ML^(2))/(8pi^(2))`

Discussion

185.	`I` is moment of inertia of a thin circular ring about an axis perpendicular to the plane of ring and passing through its centre. The same ring is folded into `2` turns coil. The moment of inertia of circular coil about an axis perpendicular to the plane of coil and passing through its centre isA. `2I`B. `4I`C. `I/2`D. `I/4`
Answer» Correct Answer - D Mass is same, `l=2pirnrArrr alpha1/n` where `n` is number of turns `Ipropr^(2)` and `(I_(1))/(I_(2))=((r_(1))/(r_(2)))^(2)=((n_(2))/(n_(1)))^(2)`

Discussion

186.	`M` is mass and `R` is radius of a circular ring. The moment of inertia of same ring about an axis in the plane of ring at a perpendicular distance `2R/3` from centre of ring isA. `(2MR^(2))/3`B. `(4MR^(2))/9`C. `(3MR^(2))/8`D. `(17 MR^(2))/18`
Answer» Correct Answer - D `I=I_(c)=+Md^(2), I_(C)=MR^(2)` and `d=(2R)/3`

Discussion

187.	The mass of a circular ring is `M` and its radius is `R`. Its moment of inertia about an axis in the plane of ring at perpendicular distance `R//2` from centre of ring isA. `(MR^(2))/4`B. `(MR^(2))/2`C. `(3MR^(2))/2`D. `(3MR^(2))/4`
Answer» Correct Answer - D `I=I_(C)+md^(2),I_(C)=(MR^(2))/2, d=R/2`

Discussion

188.	A wheel of radius `R`, mass `m` with an axle of radius `r` is placed on a horizontal surface. Its moment of inertia is `I=mR^(2)`. Unwinding a rope from its axel a force `F` is applied to pull it along a horizontal surface. The friction is sufficient enough for its pure rolling `(angletheta=0^(@))` Find the linear acceleration of the wheelA. `(F[I//m-Rr])/([(I//m)+r^(2)])`B. `(2F[(I//m)-Rr])/([(1//m)+r^(2)])`C. `(F[(2I//m)-sqrt(2)Rr])/([(I//m)+r^(2)])`D. `(F[(Isqrt(2)//m)-Rr])/([(I//m)+r^(2)])`
Answer» Correct Answer - A `F-f ma, F(r)+f(R)=Ialpha` `a=Ralpha` Solving `a=(F(r+R)R)/((R+mR^(2)))` and `f=F-ma` `=(F[(I//m)-Rr])/([(I//m)+r^(2)])`

Discussion

189.	Two bodies of different masses `2kg` and `4kg` are moving with velocities `2m//s` and `10m//s` towards each other due to mutual gravitational attraction. Then the velocity of the centre of mass isA. `5 ms^(-1)`B. `6 ms^(-1)`C. `8 ms^(-1)`D. zero
Answer» Correct Answer - D `v_(cm)=(m_(1)v_(1)+m_(2)v_(2))/(m_(1)+m_(2))`, Internal force does not change the position of centre of mass

Discussion

190.	If two particles of masses `3kg` and `6kg` which are at rest are separated by a distance of `15 m`. The two particles are moving towards each other under a mutual force of attraction. Then the ratio of distances travelled by the particles before collision isA. `2:1`B. `1:2`C. `1:3`D. `3:1`
Answer» Correct Answer - A `m_(1)r_(1)=m_(2)r_(2)`

Discussion

191.	A thin rod of length `L` is vertically straight on horizontal floor. This rod falls freely to one side without slipping of its bottom. The linear velocity of centre of rod when its top end touches floor isA. `sqrt(2gL)`B. `sqrt((3gL)/2)`C. `sqrt(3gL)`D. `sqrt((3gL)/4)`
Answer» Correct Answer - D `omega=sqrt((3g)/L,v=romega` and `r=L/2`

Discussion

192.	Two bodies of masses `5kg` and `3kg` are moving towards each other with `2ms^(-1)` and `4ms^(-1)` respectively. Then velocity of centre of mass isA. `0.25 ms^(-1)` towards `3kg`B. `0.5ms^(-1)` towards `5kg`C. `0.25 ms^(-1)` towards`5 kg`D. `0.5 ms^(-1)` towards `3 kg`
Answer» Correct Answer - C `v_(cm)=(m_(1)v_(1)+m_(2)v_(2))/(m_(1)+m_(2))`

Discussion

193.	A heavy wheel of radius `20 cm` and weight `10 kg` is to be dragged over a step of height `10 cm`, by a horizontal force `F` applied at the centre of the wheel. The minimum value of `F` isA. `20 kg w t`B. `1 kg wt`C. `10 sqrt(3) k g w t`D. `10sqrt(2) kg wt`
Answer» Correct Answer - C Clockwise torque=anticlockwise torque `mgsqrt((20)^(2)-(10)^(2))=F(20-10)`

Discussion

194.	A uniform square plate `S (side c)` and a unifrom rectangular plate `R(side b,a)` have identical areas and mass [Fig.] Show that (i) `I_(xR)//I_(xS) lt 1`, (ii) `I_(yR)//I_(yS) gt 1`, (iii) `I_(zR)//I_(zS) gt 1`. A. `I_(xR)//I_(xS)lt1`B. `I_(yR)//I_(yS)gt1`C. `I_(zR)//I_(xS)gt1`D. `I_(zR)//I_(zS)=1`
Answer» Correct Answer - A By given question Area of square =Area of rectangular plate `rArrc^(2)=axxbimplies c^(2)=ab` Now by definition `(I_(xR))/(I_(xS))=(b^(2))/(c^(2)) lt 1rArrI_(xR) lt I_(xS)(b lt c)`

Discussion

195.	A uniform disc of radius R is put over another unifrom disc of radius 2R of the same thickness and density. The peripheries of the two discs touch each other. Locate the centre of mass of the system.A. at `R//3` from the centre of the bigger disc towards the centre of the smaller discB. at `R//5` from the centre of the bigger disc towards the centre of the smaller discC. at `2R//5` from the centre of the bigger disc towards the centre of the smaller disc.D. at `2R//5` from the centre of the centre of the smaller disc
Answer» Correct Answer - B Distance of `C.M.` from centre of big disc `x=(r^(2)a)/(R^(2)+r^(2))r` -radius of small disc `R`-radius of big a- distance between the centres of discs

Discussion

196.	Find the centre of mass of a unifrom (a) half-disc,(b) quarter-disc.A. `(R,R/pi)`B. `0,0`C. `(4R/pi,0)`D. `(0,(4R)/(3pi))`
Answer» Correct Answer - D The half disc can be supposed to be consisting of a large number of semicircular rings of mass `dm` and thickness `de` and radii ranging from `r=0` to `r=R` `x_(CM)=1/mint_(0)^(R)xdm=1/mint_(0)^(R)0 dm=0` `y_(cm)=1/Mint_(0)^(R)ydm=1/Mint_(0)^(R)(2r)/mxx((2M)/(R^(2))rdr)=((4R)/(3pi))` Surface area of ring `=pirdr` `dm=(2M)/(R^(2))rdr`

Discussion

197.	A ballet dancer is rotating about his own vertical axis at an angular velocity `100 rpm` on smooth horizontal floor. The ballet dancer folds himself close to his axis of rotation by which is moment of inertia decreases to half of initial moment of inertia then his final angular velocity isA. 50 rpmB. 100 rpmC. 150 rpmD. 200 rpm
Answer» Correct Answer - D `I_(1)omega_(1)=I_(2)omega_(2),I_(1)n_(1)=I_(2)n_(2)impliesn_(2)=200` rpm

Discussion

198.	If polar ice caps melt, then the time duration of one dayA. increasesB. decreasesC. does not changeD. zero
Answer» Correct Answer - A

Discussion

199.	A ballet dancer is rotating at angular velocity `omega` on smooth horizontal floor. The ballet dancer folds his body close to his axis of rotation by which his radius of gyration decreases by `1//4^(th)` of his initial radius of gyration, his final angular velocity isA. `(3 omega)/4`B. `(9 omega)/4`C. `(9 omega)/16`D. `(16 omega)/9`
Answer» Correct Answer - D `I_(1)omega_(1)=I_(2)omega_(2),mk_(1)^(2)omega_(1)=mk_(2)^(2)omega_(2),k_(1)^(2)omega_(1)=(3/4k_(1))^(2)omega_(2)`

Discussion

200.	A unifrom disc of radius `R`, is resting on a table on its rim. The coefficient of friction between disc and table is `mu` Fig. Now the disc is pulled with a force `F` as shown in the Fig. What is the maximum value of `F` for which the disc rolls without slipping ? A. `F_(max)=3 muMg`B. `F_(max)=muMg`C. `F_(max)=5muMg`D. `F_(max)=5 Mg`
Answer» Correct Answer - A `fR=Ialpha` `=(1/2MR^(2))a/R` `:. F=F//3` `f`=frictional force `F`=pulling force

Discussion

Explore topic-wise InterviewSolutions in .

A disc of mass `m` and radius `r` placed on a routh horizontal surface. A cue of mass `m` hits the disc at a height `h` from the axis passing through centre and parallel to the surface. The disc will start pure rolling for.A. `hltr/3`B. `h=r/2`C. `hgtr/2`D. `hger/2`

Moment of inertia of a hoop suspended from a peg about the peg isA. `MR^(2)`B. `(MR^(2))/2`C. `2MR^(2)`D. `(3MR^(2))/2`

A hoop of mass `500gm` & radius `10cm` is placed on a nail, then the moment of inertia of the hoop, when it is rotated about the nail will be ____`kgm^2`A. `0.05`B. `0.02`C. `0.01`D. `0.03`

The moment of inertia of a wheel of radius `20 cm` is `40 kgm^(2)` if a tangential force of `80 N` applied on the wheel, its rotational `K.E.` after `4s` isA. `16.2J`B. `51.2J`C. `25.6 J`D. `24.8J`

A wheel has a speed of `1200` revolution per minute and is made to slow down at a rate of `4 rad//s^(2)`. The number of revolutions it makes before coming to rest isA. `143`B. `272`C. `314`D. `722`

A fly wheel of `M.I. 6xx10^(-2) kgm^(2)` is rotating with an angular velocity of `20 rad s^(-1)`. The torque required to bring it to rest in `4s` isA. `1.6 Nm`B. `0.6 Nm`C. `0.8 Nm`D. `0.3 Nm`

A gymnast standing on a rotating stool with his arms outstretched, suddenly lowers his armsA. his angular velocity decreasesB. his angular velocity increasesC. his moment of inertia remains sameD. his moment of inertia increases

The area of the triangle whose adjacent sides are represented by the vector `(4hat i + 3 hat j + 4 hat k)` and `5hat i` in sq. units isA. `25`B. `12.5`C. `50`D. `45`

The are of the parallelogram whose adjacent sides are `P=3hat i + 4 hat j, Q = -5 hat i + 7hat j` is (in sq. units)A. `20.5`B. `82`C. `41`D. `46`

The angular velocity of a rotating body is `vec omega = 4 hat i + hat j - 2 hat k`. The linear velocity of the body whose position vector `2hati + 3 hat j - 3 hat k` isA. `5 hati+8 hatk+14 hatk`B. `3hati+8hatj+10 hatk`C. `8hati-3hatj+2 hatk`D. `-8hati+3hatj+2hatk`

The unit vector perpendicular to `vec A = 2 hat i + 3 hat j + hat k` and ` vec B = hat i - hat j + hat k` isA. `(4hati-hatj-5hatk)/(sqrt(42))`B. `(4hati-hatj+5hatk)/(sqrt(42))`C. `(4hati+hatj+5hatk)/(sqrt(42))`D. `(4hati+hatj-5hatk)/(sqrt(42))`

The position of a particle is given by `vec r = hat i + 2hat j - hat k` and its momentum is `vec p = 3 hat i + 4 hat j - 2 hat k`. The angular momentum is perpendicular toA. `x`-axisB. `y`-axisC. `z-`axisD. line at equal angles to all the axes

The linear and angular velocities of a body in rotatory motion are `3 ms^(-1)` and `6 rad//s` respectively. If the linear acceleration is `6 m//s^2` then its angular acceleration in `rad s^(-2)` isA. `6`B. `10`C. `12`D. `2`

Two point P and Q. diametrically opposite on a disc of radius R have linear velocities v and 2v as shown in figure. Find the angular speed of the disc.A. `v/R`B. `(2v)/R`C. `v/(2R)`D. `v/(4R)`

A particle of mass `m` is moving in a plane along a circular path of radius `r`. Its angular momentum about the axis of rotation is `L`. The centripetal force acting on the particle is.A. `(L^(2))/(mr)`B. `(L^(2)m)/r`C. `(L^(2))/(mr^(2))`D. `(L^(2))/(mr^(2))`

Four particles each of mass `m` are placed at the corners of a square of side length `l`. The radius of gyration of the system about an axis perpendicular to the plane of square and passing through its centre isA. `l/(sqrt(2))`B. `l/2`C. `l`D. `sqrt(2)l`

Four particles each of mass `m` are placed at the corners of a square of side length `l`. The radius of gyration of the system the moment of inertia of four bodies about an axis perpendicular to the plane of frame and passing through a corner isA. `ML^(2)`B. `2ML^(2)`C. `2sqrt(2)ML^(2)`D. `4ML^(2)`

A uniform box is kept on a rough inclined plane. It begins to topple when `theta` is equal to: A. `30^(@)`B. `60^(@)`C. `tan^(-1)(1/2)`D. `45^(@)`

A square is made by joining four rods each of mass `M` and length `L`. Its moment of inertia about an axis PQ, in its plane and passing through one one of its corner isA. `6ML^(2)`B. `4/3 ML^(2)`C. `8/3 ML^(2)`D. `10/3 ML^(2)+`

The moment of inertia of `HCl` molecule about an axis passing through its centre of mass and perpendicular to the line joining the `H^+` and `Cl^-` ions will be (if the inter atomic distance is `1A^@`)

Moment of inertia of body depends uponA. distribution of mass of the bodyB. position of axis of rotationC. temperature of the bodyD. all of the above

Of the two eggs which have identical sizes, shapes and weights, one is raw and other is half boiled. The ratio between the moment of inertia of the raw to the half boiled egg about central axis is:A. `=1`B. `gt1`C. `lt1`D. not comparable

A uniform cylinder has radius `R` and length `L`. If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular face is `mg` equal to the moment of inertia of the same cylinder about an axis passing through its centre and normal to its length, then

The moment of inertia of a solid cylinder about its natural axis is `I`. If its moment of inertia about an axis `bot^r` to natural axis of cylinder and passing through one end of cylinder is `191//6` then the ratio of radius of cylinder and its length isA. `1:2`B. `1:3`C. `1:4`D. `2:3`

Two identical circular plates each of mass `0.1 kg` and radius `10cm` are joined side by side as shown in figure. Their moment of inertia about an axis passing through their common tangent is A. `1.25xx10^(-3) kg m^(2)`B. `2.5xx10^(-3) kg m^(2)`C. `1.25 xx10^(-2) kgm^(2)`D. `2.5xx10^(-2) kg m^(2)`

Two identical circular plates each of mass `M` and radius `R` are attached to each other with their planes `bot^r` to each other. The moment of inertia of system about an axis passing through their centres and the point of contact isA. `(MR^(2))/4`B. `(5MR^(2))/4`C. `3/4 MR^(2)`D. `MR^(2)`

A thin wire of length L and uniform linear mass density `rho` is bent into a circular loop with centre at O as shown. The moment of inertia of the loop about the axis XX is`

A thin rod of length `L` of mass `M` is bent at the middle point `O` at an angle of `60^@`. The moment of inertia of the rod about an axis passing through `O` and perpendicular to the plane of the rod will be A. `(ML^(2))/6`B. `(ML^(2))/12`C. `(ML^(2))/24`D. `(ML^(2))/3`

`I` is moment of inertia of a thin circular plate about its natural axis. The moment of inertia of a circular ring whose mass is half of mass of plate but radius is twice the radius of plate about an axis passing through any tangent of ring in its plane isA. `3I`B. `4I`C. `6I`D. `1.5 I`

A thin rod of mass `M` and length `L` is bent into a circular ring. The expression for moment of inertia of ring about an axis passing through its diameter isA. `(ML^(2))/(2pi^(2))`B. `(ML^(2))/(4 pi^(2))`C. `(ML^(2))/(8pi^(2))`D. `(ML^(2))/(pi^(2))`

`M` is mass and `R` is radius of a circular ring. The moment of inertia of same ring about an axis in the plane of ring at a perpendicular distance `2R/3` from centre of ring isA. `(2MR^(2))/3`B. `(4MR^(2))/9`C. `(3MR^(2))/8`D. `(17 MR^(2))/18`

The mass of a circular ring is `M` and its radius is `R`. Its moment of inertia about an axis in the plane of ring at perpendicular distance `R//2` from centre of ring isA. `(MR^(2))/4`B. `(MR^(2))/2`C. `(3MR^(2))/2`D. `(3MR^(2))/4`

Two bodies of different masses `2kg` and `4kg` are moving with velocities `2m//s` and `10m//s` towards each other due to mutual gravitational attraction. Then the velocity of the centre of mass isA. `5 ms^(-1)`B. `6 ms^(-1)`C. `8 ms^(-1)`D. zero

If two particles of masses `3kg` and `6kg` which are at rest are separated by a distance of `15 m`. The two particles are moving towards each other under a mutual force of attraction. Then the ratio of distances travelled by the particles before collision isA. `2:1`B. `1:2`C. `1:3`D. `3:1`

A thin rod of length `L` is vertically straight on horizontal floor. This rod falls freely to one side without slipping of its bottom. The linear velocity of centre of rod when its top end touches floor isA. `sqrt(2gL)`B. `sqrt((3gL)/2)`C. `sqrt(3gL)`D. `sqrt((3gL)/4)`

Two bodies of masses `5kg` and `3kg` are moving towards each other with `2ms^(-1)` and `4ms^(-1)` respectively. Then velocity of centre of mass isA. `0.25 ms^(-1)` towards `3kg`B. `0.5ms^(-1)` towards `5kg`C. `0.25 ms^(-1)` towards`5 kg`D. `0.5 ms^(-1)` towards `3 kg`

A heavy wheel of radius `20 cm` and weight `10 kg` is to be dragged over a step of height `10 cm`, by a horizontal force `F` applied at the centre of the wheel. The minimum value of `F` isA. `20 kg w t`B. `1 kg wt`C. `10 sqrt(3) k g w t`D. `10sqrt(2) kg wt`

Find the centre of mass of a unifrom (a) half-disc,(b) quarter-disc.A. `(R,R/pi)`B. `0,0`C. `(4R/pi,0)`D. `(0,(4R)/(3pi))`

If polar ice caps melt, then the time duration of one dayA. increasesB. decreasesC. does not changeD. zero