Centre Of Mass MSQ

# Centre Of Mass MSQ

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## 10 Questions MCQ Test Topic wise Tests for IIT JAM Physics | Centre Of Mass MSQ

Centre Of Mass MSQ for IIT JAM 2022 is part of Topic wise Tests for IIT JAM Physics preparation. The Centre Of Mass MSQ questions and answers have been prepared according to the IIT JAM exam syllabus.The Centre Of Mass MSQ MCQs are made for IIT JAM 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Centre Of Mass MSQ below.
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*Multiple options can be correct
Centre Of Mass MSQ - Question 1

### When a block is placed on a wedge as shown in the figure, the block starts sliding down and the wedge  also start sliding on ground. All surfaces are rough. The centre of mass of (Wedge + block) system will move :

Detailed Solution for Centre Of Mass MSQ - Question 1

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

*Multiple options can be correct
Centre Of Mass MSQ - Question 2

### Assuming potential energy U at ground level to be zero. All objects are made up of same material UP = Potential energy of solid sphere UQ = Potential energy of solid cube UR = Potential energy of solid cone US = Potential energy of solid cylinder

Detailed Solution for Centre Of Mass MSQ - Question 2

centre of mass of cone is on smallest height.

The correct answers are: US > UPUQ >USUS > UR

*Multiple options can be correct
Centre Of Mass MSQ - Question 3

### Two particles A and B start moving due to their mutual interaction only. If any time t,  are their respective acceleration, are their respective velocities and upto that time WA and WB are the work done on A and B respectively by the mutual force, mA and mB are their masses respectively, then which of the following is always incorrect.

Detailed Solution for Centre Of Mass MSQ - Question 3

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

*Multiple options can be correct
Centre Of Mass MSQ - Question 4

The diagram shows the velocity-time graph for two masses  R and S that collided elastically. Which of the following statement is true?

Detailed Solution for Centre Of Mass MSQ - Question 4

(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

*Multiple options can be correct
Centre Of Mass MSQ - Question 5

A particle strikes a horizontal smooth floor with a velocity u making an angle  with the floor and rebounds with velocity v making and angle  with the floor. If the coefficient of restitution between the particle and the floor is e,  then :

Detailed Solution for Centre Of Mass MSQ - Question 5

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

*Multiple options can be correct
Centre Of Mass MSQ - Question 6

A bag of mass M hangs by a long thread and a bullet (mass m) comes horizontally with velocity v and gets caught in the bag. Then for the combined system (bag + bullet) which of the following are correct

Detailed Solution for Centre Of Mass MSQ - Question 6

Since, Fext = 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

*Multiple options can be correct
Centre Of Mass MSQ - Question 7

A ball of mass m moving with a velocity v hits a massive wall of mass M (M >> m) moving towards the ball with a velocity u. An elastic impact lasts for a time  Δt. Which of the following are correct.

Detailed Solution for Centre Of Mass MSQ - Question 7

In an elastic collision
vsep = vapp

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)

*Multiple options can be correct
Centre Of Mass MSQ - Question 8

Two blocks of equal mass m are connected by an unstretched spring and the system is kept at rest on a frictionless horizontal surface. A constant force F is applied on the first block pulling it away from the other as shown in figure.

Detailed Solution for Centre Of Mass MSQ - Question 8

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

*Multiple options can be correct
Centre Of Mass MSQ - Question 9

For a two-body system in absence of external forces, the kinetic energy as measured from ground frame is K0 and from centre of mass frame is Kcm. Pick up the correct statement.

Detailed Solution for Centre Of Mass MSQ - Question 9

It can be shown that

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

Due to internal changes Kcm can change but Vcm will remain same. Hence only Kcm 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 Kcm can be transformed from one form to another due to internal changes in the system., The system always retains at least K0Kcm amount of kinetic energy as measured from ground frame irrespective of any kind of internal change in the system.

*Multiple options can be correct
Centre Of Mass MSQ - Question 10

A smooth sphere A of mass m collides elastically with an identical sphere B at rest. The velocity of A before collision is 8 m/s in a direction making 60° with the line joining the centre at the time of impact. Which of the following is/are possible :

Detailed Solution for Centre Of Mass MSQ - Question 10

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

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