Displacement of COM:Application

Q. A uniform chain of length 4 m is kept on a table such that a length of 120 cm hangs freely from the edge of the table.The total mass of the chain is 4 kg.What is the workdone in pulling the entire chain on the table?

Q. A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain cons†an t for sphe 1)angular velocity 2)moment of inertia 3)rotational kinetic energy 4)angular momentum

Q.

A child sits stationary at one end of long trolley moving uniformly with speed v on a smooth horizontal floor. If the child gets up and runs about on the trolley in the forward direction with speed u. The centre of mass of the system (child + trolley) will move with speed

1. u + v

2. zero

3. v / u

4. v

Q.

A 2kg block is dropped from a height of 0.4 m on a spring of force constant K = 1960 Nm−1. The maximum compression of the spring is

0.1 m

0.2 m

0.3 m

0.4 m

Q. 32. A 1 kg stationary bomb is exploded in three parts having masses in ratio 1:1:3 respectively parts having same mass move in perpendicular direction with velocity 30m/s , then the velocity of bigger part will be?

Q. A particle of mass 2kg located at position (i + j) units has velocitu 2(i-j+k) units its angular momentum about origin is

Q. Q. A Body of mass 1 kg is attached to one end of a wire and rotated in a horizontal circle of diameter 40cm with a cons†an t speed of 2m/s. what is the area of cross section of wire. if the stress developed in the wire is 5\ast10^6 N/m^2.

Q. If K.E. increases by 3%. Then momentum willincrease by:21.(1) 1.5%(2) 9%Tots(4) 2%(3) 3%

Q. Three bricks each of length L and mass M are arranged as shown. The distance of the centre of mass of the system from the wall is :- Wall k-L2→

Q. A particle of mass 3kg is moving along x-axis and its position at time t is given by equation x=(2t^2+5)m. Work done by all the forces acting on it in time interval t=0 to t=3 s is .

Q. When a load of 10kg is hung from the wire, then extension of 2m is produced.Then the work done by restoring force is?Explain in detail

Q. { A }2 kg mass lying on a table is displaced in the }}{ horizontal directionthrough }50cm . The work done }} by the normal reaction will be -

Q. a particle of mass m moves on a straight line with its velocity varying with the distance travelled . if the relation between velocity and disatnce is v =kx . then find the work done by the force during a dispalcemnet x=0 to x= d

Q. A force (mv^2/r) is acting on a body of mass m moving with a velocity v ina circle of radius r. what is the work done by the force in moving the body over half the circumference of the circle?

Q.

A battle ship simultaneously fires two shells at enemy ships. Both are fired with the same speed but with different directions as shown. If the shells follow the parabolic trajectories shown, which ship gets hit first?

1. Need more information about the trajectories.

2. Ship μ1

3. They get hit at the same time.

4. Ship μ2

Q.

A rod of mass m and length l is kept on a smooth wedge of mass M as shown in the figure. If the system is released, find the speed of the wedge when the rod hits the ground level, neglecting friction in all contacting surfaces.

1. =

2. =

3. =

4. None of these

Q. 50. Two objects of mass 1 kg and 2 kg are fixed at a certain distance between them. if a mass of 4 kg is placed between them , , attains equilibrium at a distance r from the smaller mass then its distance from the larger mass will be?

Q. Two persons of masses m and 2m are s†an ding on a horizontal smooth surface. They are initially separated by a dis†an ce X_o. They slide on the horizontal surface as they pull a rope towards each other. they meet at what dis†an ce?

Q. 15.Three particle of masses m1-1.2kg, m2-2.5kg, m3-3.4kg form an equilateral triangle of edge length a=140cm. what is the centre of mass of three particles?

Q. a projectile of mass m is fired with velocity v at an angle θ with the horizontal. What is the change in momentum as it rises to the highest point of its trajectory

Q. 29. In each of the following a force F is acting on an object of mass m. The direction of displacement is from west to east shown by the longer arrow. Observe the diagrams carefully and state whether the work done by the force is negative, positive or zero by giving reason.

Q. 45. A bucket tied to a string is lowered at a constant acceleration of g/4. If the mass of the bucket is M and lowered by a distence d, the work done by the string on the bucket will be what? (assume the string to be massless)

Q.

Inside a hollow uniform sphere of mass M , a uniform rod of lenght R$\sqrt{2}$ is released from the state of rest. The mass of the rod is same as that of the sphere. If the inner radius of the hollow sphere is R then find out horizontal displacement of sphere with respect to earth in the time in which the rod becomes horizontal.

1. 

2. 
   

3. 

4. 

Q.

Two children sit on a see-saw which is 6 m long and pivoted on an axis at its center. The first child has a mass of 20 kg and sits at the left end of the see-saw, while the second child has a mass of 40 kg and sits somewhere on the see-saw to the right of the axis. At what distance from the axis should the second child sit to keep the see-saw horizontal?

1. 1 m

2. 1.5 m

3. 2.5 m

4. 3 m

Q.

A block of mass $m_1=2kg$ slides along a frictionless table with a speed of 10m/s. Directly in front of it, and moving in same direction is a block of mass $m_2=5kg$ moving at a speed of 3 m/s. A massless spring with a constant of k = 1120 N/m is attached to the back side of $m_2$ as shown. When the block collides, what is the maximum compression in the spring?

1. 0.25 m

2. 0.50 m

3. 0.125 m

4. 0.75 m

Q. A stationary body explodes into two fragmrnts of masses m1 and m2. if momentum of one fragment is p, the energy of explosion is-1)p^2/2(m1+m2), 2)p^2/2\surd(m1m2), 3)p^2(m1+m2)/2(m1m2), 4)p^2/2(m1-m2).

Q. Two thin circular discs of mass m and 4m. having radii a and 2a laid on a firm and flat surface, and set roling without slipping on the surface so that the angular speed about the of the rod s a The angular momentum of the entreassembly about the point O is L (see the figure). Which ofhe folowing statement (s) is (are) true(JEE (Advanced) 20164mTR0

Q. 2.Find the magnitude of change in momentum of an oblique projectile during its whole journey its velocity and angle of projection are v_0 and θ_0 respectively.

Q. a chain of mass m and length L is held on a frictionless table such that 1/nth part hangs below. calculate work done to pull the hanging part of the chain.

Q. a body of mass 300kg is moved through 10m along a smooth inclined plane of angle 30degree.the work done in moving in joules is