InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
Two blocks `A` and `B` of masses `m` and `2m` are placed on a smooth horizontal surface. Block `B` is given a speed of `3m//s`. Find `(i)` The maximum speed of `A` `(ii)` The minimum speed of `B`. |
| Answer» `(i) 4m//s`, `(ii) 1m//s` | |
| 52. |
Two blocks of mass `2kg` and `4kg` are given speed `3m//s` and `2m//s` respectively on a rough surface with coefficient of friciton `0.2`. Find the distance travelled and displacement of the centre of mass after a long time. |
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Answer» Distance travelled `=(1)/(4)m` Displacement `=(1)/(12)m` (towards left) |
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| 53. |
A collar `B` of mass `m` is at rest and when it is in the position shown, the spring is unstretched. If another collar `A` of mass `(m)/(n)` strikes it so that `B` slides a distance `4m` on the smooth rod before momentarily stopping, determine the velocity of `A` just after the impact. The coefficient of restitution is `e`. The spring constant is `k`. |
| Answer» `2(1-etae)/(1+e)sqrt((k)/(m))` | |
| 54. |
A block of mass `m` is released from a wedge of mass `m` as shown in figure . Find the time taken by the block to reach the end of the wedge. |
| Answer» Correct Answer - `sqrt((7h)/(3g))` | |
| 55. |
A bob of mass `m` is hanging from a cart of mass `M`. System is relased from rest from the position shown. Find the maximum speed of the cart with respect to ground. |
| Answer» `sqrt((m^(2)gl)/(M(m+M)))` | |
| 56. |
A sphere of mass `m` and radius `R` is dropped from the top of a fixed rough wedge of height `h`. Find the maximum height to which the sphere rises on a smooth movable wedge of mass `m` lying adjacent to the fixed wedge on smooth ground. |
| Answer» `(5Mh+R(7m+2M))/(m+M)` | |
| 57. |
A uniform rod is lying against a smooth wall and on a smooth floor. It is relased from rest when it makes an angle `theta_(0)` with the ground. Find the angle rod will make with the ground it just leaves the contact with the walls. |
| Answer» `sin^(-1)((2)/(3)sintheta_(0))` | |
| 58. |
A particle of mass `m` is dropped in side a spherical shell of mass `2m` and radius `R` as shown in figure. If the collision is perfectly in elastic and fricition is absent everywhere then find the maximum speed of the centre of the sphere. |
| Answer» Correct Answer - `sqrt((29)/(66)gR)` | |
| 59. |
A uniform rod of length `l` is slightly disturbed from its vertical position. Find the angular velocity of the rod just after if hits the step. (Friction is sufficient everywhere to prevent slipping) |
| Answer» `(10)/(7)sqrt((3g)/(2l))` | |
| 60. |
A particle of mass `m` collides with a uniform rod of mass `M` and length `L` as shown in figure. If initial speed of the particle was `u`. Find the final velocity vector of the rod and particle just after collision.(The complete system is in horizontal plane) |
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Answer» `v_(rod)=((1+e)mucostheta)/((M+m))hati` `v_("particle")=(e-(m)/(M))(Mucostheta)/((M+m))(-hati)+usinthetahatj` |
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| 61. |
A particle collides a horizontal smooth surface with velocity `vecv_(1)`, `hatn` is the unit vector perpendicular to the surface. If `e` is the coefficient of restitution, then find the velocity vector in which particle is rebounded. |
| Answer» `vecv_(1)-[vecv_(1)*hatn)(1+e)]hatn` | |
| 62. |
Three point masses of `1kg`, `2kg` and `3kg` lie at `(0,0)`, `(1,2)`, `(3,-1)` respectively. Calculate the coordinates of the centre of mass of the system. |
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Answer» `x_(cm)=(1xx0+2xx1+9)/(6)=(11)/(6)` `y_(cm)=(1xx0+2xx2-1xx3)/(6)=(4-3)/(6)=(1)/(6)` `(x_(cm),y_(cm))=((11)/(6),(1)/(6))` |
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| 63. |
The coordinates of a triangle `ABC` are `A(1,2)`, `B(4,6)` and `C(-3,-2)`. Three particles of masses `1kg`, `2kg` and `m kg` are placed the vertices of the triangle. If the coordinate of the centre of mass are `((3)/(5),2)`, calculate the mass `m`. |
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Answer» `x_(cm)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3))/(m_(1)+m_(2)+m_(3))=(3)/(5)` `implies(1+8-3m)/(3+m)=(3)/(5)` `implies(9-3m)/(3+m)=(3)/(5)` `implies45-15m=9+3m` `implies36=18m` `impliesm=2 kg` Or Alternate method `y_(cm)=(m_(1)y_(1)+m_(2)y_(2)+m_(3)y_(3))/(m_(1)+m_(2)+m_(3))=2` `implies(2+12-2m)/(3+m)=2` `implies14-2m=6+2m` `implies8=4m` `m=2kg` |
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