Why Com Is an Important Point

Q.

Two blocks A and B of equal mass m=1 kg are lying on a smooth horizontal surface as shown below A spring of force constant k = 200 N/m is fixed at one end of block 'A'. Block 'B' collides with 'A' with velocity V₀ = 2 m/s. The maximum compression of the spring is

1. 12 cm

2. 14 cm

3. 16 cm

4. 10 cm

Q. 83. A solid sphere of radius R is placed on a smoothhorizontal surface. A horizontal force F is applied atheight h from the lowest point. For the maximumacceleration of centre of mass, which is correct?(1) h R(2) h=2R(3) h=0(4) Centre of mass has same acceleration ineach case

Q. 10. A uniform sphere is placed on a smooth horizontalsurface and a horizontal force Fis applied on it at adistance h above the surface. The acceleration of thecentre(a) is maximum when h =0(b) is maximum when h R(c) is maximum when h=2R(d) is independent of h.

Q. Two masses A and B of mass 4 kg and 1 kg respectively are connected with the help of massless inextensible string. Mass A is placed on a rough horizontal table and mass B is hanging with the help of string passing through a smooth hole at the centre of table. For the system to be in equilibrium what can be the minimum value of coefficient of friction?(1) 0.5(2) 0.25(4) 0.125(3) 2.5

Q. 40.A particle of mass m is kept on the top of a smooth sphere of radius R .it is given a sharp impulse which imparts it a horizontal speed V.what should be the minimum value of v for which the particle does not slip on the sphere?(with full reason)

Q. A small ball strikes at one end of a stationary uniform frictionless rod of mass m andlength I which is free to rotate, in gravity-free space. The impact is elastic. Instantaneous axis of rotation of the rod will pass through(A) its center of mass.(B) the center of mass of rod plus ball.(C) the point of impact of the ball on the rod.(D) the point which is at a distance 2l/3 from the striking end.

Q. 53.A ball of mass 1 kg strikes a wall with velocity 1m/s at an angle of 60^° with the wall and reflects at the same angle. If it remains contact with wall for 0.1 second then the force is

Q. 64.A man of mass M stands at one end of a plank of length L which lies at rest on frictionless surface. The man walks on the other end of plank. If mass of plank is M/3 the distance man moves relative to the ground is

Q. 59. Balls are being thrown with speed u at an angle theta with horizontal at the rate n balls per second. Mass of each ball is m . What is the average force exerted by the balks at point P. (

Q. An iron ball of mass 100 gm moving at a speed of 10 m/sec strikes a wall at angle of 30 degree and reflects at the same angle . If ball and wall remain in contact for 0.1sec, the force exerted on the wall will be how much

Q. 6. A one kg particle strikes a few A one kg particle strikes a wall with velocity onem/s at an angle of 30degree with normal to the wall and reflects at the same angle. If it Remain in contact with wall for 0.1 sec then the force is

Q. A sphere of mass m , moving with a velocity V, enters a hanging bag of sand and stops. If the mass of the bag is M and is raised by a height h; then find the velocity of sphere in terms of m, M and h

Q. Two blocks of masses $3\text{kg}$and $6\text{kg}$ respectively are placed on a smooth horizontal surface. They are connected by a light spring of force constant $k=200\text{N/m}$. Initially the spring is unstretched. The indicated velocities are imparted to the blocks. Find the maximum extension of the spring.

1. $30\text{cm}$
2. $60\text{cm}$
3. $15\text{cm}$
4. $90\text{cm}$

Q. Which of the following statements are correct?
a) Centre of mass of a body always coincides with the centre of gravity of the body.
b) Centre of mass of a body is the point at which the total gravitational torque on the body is zero.
c) A couple on a body produce both translational and rotation motion in a body.
d) Mechanical advantage greater than one means that small effort can be used to lift a large load.

1. (a) and (b)
2. (b) and (c)
3. (c) and (d)
4. (b) and (d)

Q. a small ball of mass M is a dis†an ce R / 2 from the centre of a uniform spherical body of mass M .The force exerted on the small ball is (R is the radius of the sphere)

Q. Two objects are moving on a surface.The center of mass exists only if -

1. the two objects are physically connected
2. the surface is level
3. the surface is frictionless
4. There is always a center of mass.

Q. A particle of mass m is kept on a fixed, smooth sphere of radius R at a position where the radius through the particle makes an angle of 30° with the vertical. The particle is released from this position. (a) What is the force exerted by the sphere on the particle just after the release? (b) Find the distance travelled by the particle before it loses contact with the sphere.

Q. A uniform sphere is placed on a smooth horizontal surface and a horizontal force F is applied on it at a distance h above the surface. The acceleration of the center

1. Is Maximum when h=0
2. is maximum when h=R
3. is maximum when h=2R
4. is independent of h.

Q. Seven identical geese are flying south together at constant speed. A hunter shoots one of them, which immediately dies and falls to the ground. The other six continue flying south at the original speed. After the one goose has hit the ground, the center of mass of all seven geese

1. Continues south at the original speed, but is now located some distance behind the flying geese.
2. Continues south, but at $\frac{6}{7}$ the original speed.
3. Continues south, but at $\frac{1}{7}$ the original speed.
4. Stops with the dead goose.