Centre Of Mass MSQ - IIT JAM MCQ

Friction force between wedge and block is internal i.e. will not change motion of centre of mass. Friction force on the wedge by ground is external and causes centre of mass to move towards right. Gravitational force (mg) on block brings it downward hence centre of mass comes down.

The correct answer is: rightward and downward

centre of mass of cone is on smallest height.

The correct answers are: U_S > U_P, U_Q >U_S, U_S > U_R

Since  ∴  Momentum of system will remain conserved, equal to zero.

The correct answers are:  

(i) Since, both have positive final velocities, hence, both moved in the same direction after collision.

(ii) at t = 2 sec. both had equal velocities.

(iii) by conservation of linear momentum, we can say that mass of R was greater than mass of S.

The correct answers are: R and S moved in the same direction after the collision, The velocities of R and S were equal at the mid time of the collision, The mass of R was greater than mass of S

In horizontal direction, momentum is conserved :

in vertical direction,

The correct answers are: the impulse delivered by the floor to the body is   the ratio of the final kinetic energy to the initial kinetic energy is 

Since, F_ext = 0
Hence, momentum will remain conserved equal to mv.

and final kinetic energy is 

The correct answers are: Momentum is mv, KE is m²v²(M + m)/2

In an elastic collision
v_sep = v_app

change in momentum of ball is 

= 2m(u + v)

The correct answers are: The average elastic force acting on the ball is  The kinetic energy of the ball increase by 2mu(u+v)

The acceleration of the centre of mass is

The displacement of the centre of mass at time t will be

Therefore initial velocity is either in direction of constant force or opposite to it. Hence the particle will move in straight line and speed may increase or decrease. When F and u are antiparallel then particle will come to rest for an instant and will return back.

Initial velocity is perpendicular to constant force, hence the path will be parabolic with speed of particle increasing.  means instantaneous velocity is always perpendicular to force. Hence the speed will remain constant. And also  constant. Since the particle moves in one plane, the resulting motion has to be circular.  Hence initial velocity is in same direction of constant acceleration, therefore, particle moves in straight line with increasing speed.

The correct answers are: The displacement of the centre of mass at time t is  The displacement of the right block, if the extension of the spring is x₀ at time t, is  The displacement of the left block, if the extension of the spring is x₀ at time t, is 

It can be shown that

where M is the total mass of the system and V_cm is velocity of centre of mass with respect to ground.

Due to internal changes K_cm can change but V_cm will remain same. Hence only K_cm portion of kinetic energy can be transformed to some other from of energy.
The correct answers are: The kinetic energy as measured from centre of mass frame is least, Only the portion of energy K_cm can be transformed from one form to another due to internal changes in the system., The system always retains at least K₀–K_cm amount of kinetic energy as measured from ground frame irrespective of any kind of internal change in the system.

Sphere A moving with velocity v has a component v/2 along the line joining the centres of the spheres at the time of collision and another component   perpendicular to the previous direction. After collision the component along the line will interchange i.e. B will move with v/2 velocity i.e., 4 m/s along the line joining the centres and A moves with  velocity at perpendicular direction to B.

The correct answers are: the direction of motion of A and B after collision are at right angles, the speed of B after collision is 4 m/s