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601.

A conveyor belt is moving at a constant speed of `2m//s` . A box is grenty dropped on it. Th ecoefficient of friction between them is `mu=0.5` . The distance that the box will move relative to belt before coming to rest on it taking `g=10ms^(-2)` is:A. `1.2m`B. `0.6m`C. zeroD. `0.4m`

Answer» Correct Answer - D
Force, `F=mumg`
Retardation of the block on the belt
`a=(F)/(m)=(mumg)/(m)=mug`
From, `v^(2)=u^(2)+2as`
`0=(2)^(2)-2(mug)s`
`s=(4)/(2xx0.5xx10)=0.4m` .
Discussion
602.

A block kept on an inclined surface, just begins to slide if the inclination is `30^(@)`. The block is replaced by another block B and it is just begins to slide if the inclination is `40^(@)`, then :A. Mass of A `gt` mass of BB. Mass of A `lt` mass of BC. Mass of A = mass of BD. All the three are possible.

Answer» Correct Answer - D
Discussion
603.

A block `X` kept on an inclined surface just begins to slide if the inclination is `theta_(1)` The block is replaced by another block `Y` and it is found that it just begins to slide if the inclination is `theta_(2),(theta_(2) gt theta_(1))` Then .A. Mass of `X =` mass of YB. Mass of `X lt` mass of `Y`C. Mass of `X gt` mass of YD. All the three are possible .

Answer» Correct Answer - D
Discussion
604.

Gravels are dropped on a conveyor belt at the rate of `0.5` kg / sec . The extra force required in newtons to keep the belt moving at 2 m/sec isA. 1B. 2C. 4D. `0.5`

Answer» Correct Answer - A
Discussion
605.

A man of mass `65kg` is standing stationary with respect to a conveyor belt which is accelerating with `1m//s^(2)`. if `mu_(s)` is 0.2 the net force on the man and the maximum acceleration of the belt so that the man is stationary relative to the belt are `(g =10 m//s^(2))` .A. `zero, 2m//s^(2)`B. `65N,2m//s^(2)`C. `zero,1m//s^(2)`D. `65N,1m//s^(2)`

Answer» Correct Answer - A
Discussion
606.

A mass of 0.5 kg is just able to slide down the slope of an inclined rough surface when the angle of inclination is `60^(@)`. The minimum force necessary to pull the mass up the incline along the line of greatest slope is : (Take `g=10m//s^(2)`)A. 20 NB. 9 NC. 100 ND. 1 N

Answer» Correct Answer - B
Discussion
607.

A horizontal conveyor belt moves with a constant velocity `V.A` small block is projected with a velocity of `6m//s` on it in a direction opposite to the direction of motion of the belt The block comes to rest relative to the belt in a time `4s. mu =0.3, g =10 .m//s^(2)` Find `V` .

Answer» `|vecV_(b,c)|=V_(b)+V_(c)=6+V`
`f =mumg = 0.3 xx m xx 10 =3m`
Retardation ` a = (F)/(m) = (3m)/(m) =3m//s^(2)`
`u_(r) = 6 + V,V_(r) =0,t =4 sec, a_(r) = - 3ms^(-2)`
`V_(r) =u_(r) + a_(r)t, 0 =(6 +V) -3 xx 4, V =6m//s` .
Discussion
608.

A particle is projected along the line of greatest slope up a rough plane inclined at an angle of `45^(@)` with the horizontal. If the coefficient of friction is `1//2` . Their retardation is:A. `(g)/(2sqrt(2))`B. `(g)/(sqrt(2))`C. `(g)/(sqrt(2))(1-(1)/(2))`D. `(g)/(sqrt(2))(1+(1)/(2))`

Answer» Correct Answer - D
The retardation a is given by
`a=gsin45^(@)+mugcos45^(@)`
`=(g)/(sqrt(2))+(1)/(2)gxx(1)/(sqrt(2))=(g)/(sqrt(2))(1+(1)/(2))` .
Discussion
609.

A small block of mass `m` is projected on a larger block of mass `10 m` and length `l` with a velocity `v` as shown in the figure. The coefficient of friction between the two block is `mu_(2)` while that between the lower block and the ground is `mu_(1)`. Given that `mu_(2) gt 11 mu_(1)`. (a) Find the minimum value of `v`, such that the mass `m` falls off the block of mass `10 m` . (b) If `v` has minimum value, find the time taken by block `m` to do so.

Answer» Correct Answer - (a) `v_(min) = sqrt((22(mu_(1)-mu_(1))g)/(10))` (b) `t = sqrt((20l)/(11g(mu_(2)-mu_(1))))`
Discussion
610.

A ball is travelling with uniform translatory motion. This means that .A. it is at rest.B. the path can be a straight line or circular and the ball travels with uniform speed.C. all parts of the ball have the same velocity (magnitude and direction) and the velocity is constant.D. the centre of the ball moves with constant velocity and the ball spine about its centre uniformly.

Answer» Correct Answer - C
In uniform traslatory motion, all parts of the ball have the same velocity in magnitude and direction and this velocity is constant.
Discussion
611.

Theoretically which of the following are best lubricants ? .A. SolidsB. LiquidsC. GasesD. Both 2 and 3

Answer» Correct Answer - C
Discussion
612.

A force vector applied on a mass is represented as `vec(F)=6hat(i)-8hat(j)+10hat(k)` and acceleration with `m//s^(2)`. What will be the mass of the body in kg.A. `10sqrt(2)`B. 20C. `2sqrt(10)`D. 10

Answer» Correct Answer - A
`|vec(F)|=Fsqrt((6)^(2)+(-8)^(2)+(10)^(2))=10sqrt(2)N`
`F=ma=2xx2=4N`
Discussion
613.

A train is moving with velocity `20 m//sec` . on this dust is falling at the rate of 50 kg / minute . The extra force required to move this train with constant velocity will beA. `16.66` NB. 1000 NC. `166.6` ND. 1200 N

Answer» Correct Answer - A
Discussion
614.

A metal disc of radius R can rotate about the vertical axis passing through its centre. The top surface of the disc is uniformly covered with dust particles. The disc is rotated with gradually increasing speed. At what value of the angular speed `(omega)` of the disc the `75% `of the top surface will become dust free. Assume that the coefficient of friction between the dust particles and the metal disc is `mu = 0.5`. Assume no interaction amongst the dust particles.

Answer» Correct Answer - `omega = sqrt((g)/(R))`
Discussion
615.

A force-time graph for the motion of a body is shown in fig. change in linear momentum between 0 and 8 s is:- A. ZeroB. 4N-sC. 8NsD. None

Answer» Correct Answer - A
`Deltap=int Fdt=0` (area of F-t graph is zero)
Discussion
616.

Assertion : Linear momentum of a body changes even when it is moving uniformly in a circle. Reason : Force required to move a body uniformly along a straight line is zero.A. If both assertion and reason are true and the reason is the correct explanation of the assertionB. If both assertion and reason are true but reason is not the correct explanation of the assertionC. If assertion is true but reason is false.D. If the assertion and reason both are false.

Answer» Correct Answer - B
Discussion
617.

Assertion : A bullet is fired from a rifle. If the rifle recoils freely, the kinetic energy of rifle is more than that of the bullet. Reason : In the case of rifle bullet system the law of conservation of momentum violates.A. If both assertion and reason are true and the reason is the correct explanation of the assertionB. If both assertion and reason are true but reason is not the correct explanation of the assertionC. If assertion is true but reason is false.D. If the assertion and reason both are false.

Answer» Correct Answer - D
Discussion
618.

A block of mass m is supported by a string passing through a smooth peg as shown in the figure-2.130. Variation of tension in the string T as a function of `theta` best represented by (here the total length of the string is varied). A. B. C. D.

Answer» Correct Answer - B
Discussion
619.

A metal block of mass m is placed on a smooth metallic plane in support with string as shown in diagram. If after long time due to corrosiom, the contact surface becomes rough with coefficient of friction `mu`, then friction force acting on the block will be : A. `mu mg cos theta`B. `mg sun theta`C. `mg^(1)`D. None

Answer» Correct Answer - D
Discussion