Q: A ball of mass 0.5 kg is dropped from a height of 40 m . The ball hits the ground and rises to a height of 10 m . The impulse imparted to the ball during its collision with the ground is (Take g =9.8

aligned v_i & =- 2 gh _i =- 2 9.8 10 =-28 ~m / s \\ v _ f & = 2 gh _ i = 2 9.8 10 =14 ~m / s \\ I & = P = m v _ f - m v _ i \\ & = m [ v _ f - v _ i ]=0.5[14-(-28)] \\ & =0.5 42=21 NS aligned

Question 1

A frictionless circular wire of unit radius is fixed on the horizontal plane. Two point particles of unit mass start moving simultaneously from point A ( = 2 ) with identical uniform angular speeds in

Accepted Answer

Let the uniform angular speed of the particles be . The position vector of the particle on the right at an angle is given by r _1 = i + j . Since it moves from = 2 to = - 2 , its angular velocity is d dt = - . The velocity of the first particle is v _1 = d r _1 dt = (- i + j ) d dt = i - j . By symmetry, the position vector of the particle on the left is r _2 = - i + j . Its velocity is v _2 = d r _2 dt = ( i + j ) d dt = - i - j . The total linear momentum of the system is P = m v _1 + m v _2.

Question 2

Bob B of mass m at rest is hanging vertically from the ceiling via a massless string of length 10 m, as shown in the figure. Point mass A of mass m travelling horizontally with speed 10 ms^ -1 hits bo

Accepted Answer

Since the collision is elastic and the masses of A and B are equal, they will exchange their velocities upon collision. Velocity of bob B just after the collision, v = 10 ms^ -1 . By conservation of mechanical energy for bob B during its upward swing: 1 2 m v^2 = m g h Substituting the given values (v = 10 ms^ -1 , g = 10 ms^ -2 ): 1 2 m (10)^2 = m 10 h 50 = 10 h h = 5 m. Since h Answer: 5

Question 3

A ball of mass 0.5 kg is dropped from a height of 40 m . The ball hits the ground and rises to a height of 10 m . The impulse imparted to the ball during its collision with the ground is (Take g =9.8

Accepted Answer

aligned v_i & =- 2 gh _i =- 2 9.8 10 =-28 ~m / s \ v _ f & = 2 gh _ i = 2 9.8 10 =14 ~m / s \ I & = P = m v _ f - m v _ i \ & = m [ v _ f - v _ i ]=0.5[14-(-28)] \ & =0.5 42=21 NS aligned

Question 4

Two bodies A and B of same mass undergo completely inelastic one dimensional collision. The body A moves with velocity v_1 while body B is at rest before collision. The velocity of the system after co

Accepted Answer

It undergoes completely inelastic collision Using conservation of linear momentum Initial momentum = Final momentum aligned & m v_1=m v_2+m v_2 \ & m v_1=2 m v_2 \ & v_1 v_2 = 2 1 aligned

Center of Mass Momentum and Collision — Previous Year Questions & Solutions