Home
Class 12
PHYSICS
Consider a body, shown in figure, consis...

Consider a body, shown in figure, consisting of two identical balls, each of mass M connected by a light rigid rod. If an impulse J = MV is imparted to the body at one of its ends what would be it angular velocity?

A

v/L

B

(2v/L

C

v/3L

D

v/4L

Text Solution

Verified by Experts

Initial angular momentum of the system about point O = Linear momentum x Perpendicular distance of linear momentum from the axis of rotation = Mv (L/2)..(i) Final angular momentum of the system about point `O=I_1omega+I_2omega=(I_1+I_2)omega=[M(L/2)^2+M(L/2)^2]omega` (ii)Applying the law of conservation of angular momentum `rArr Mv(L/2)=2M(L/2)^2omega` `rArr omega=v/L`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Consider a system consisting of two identical balls each of mass M connected by a light rigid rod as shown in figure. An impulse J=MV is imparted to the system at one of its ends. The angular velocity of the system would be

Two identical rods each of mass m and length are connected as shown. Locate c.m.

Two small balls, each of mass m are connected by a light rigid rod of length L. The system is suspended from its centre by a thin wire of torsional constant k. The rod is rotated about the wire through an angle theta_0 and released. Find the tension in the rod as the system passes through the mean position.

Figure a rigid body consisting of two particles of mass m connected by a rod of length L and negligible mass. (a) What is the rotational inertia I_(com) about an axis through the center of mass, perpendicular to the rod as shown? (b) What is the rotational inertia I of the body about an axis through the left end of the rod and parallel to the first axis.

A uniform rod of length L and mass M is lying on a frictionless horizontal plane and is pivoted at one of its ends as shown in Fig. There is no friction at the pivot. An inelastic ball of mass m is fixed with the rod at a distance L//3 from O . A horizontal impulse J is given to the rod at a distance 2L//3 from O in a direction perpendicular to the rod. Assume that the ball remains in contact with the rod after the collision and impulse J acts for a small time interval /_\t . Now answer the following questions: Find the resulting instantaneous angular velocity of the rod after the impulse.

A uniform rod of length L and mass M is lying on a frictionless horizontal plane and is pivoted at one of its ends as shown in Fig. There is no friction at the pivot. An inelastic ball of mass m is fixed with the rod at a distance L//3 from O . A horizontal impulse J is given to the rod at a distance 2L//3 from O in a direction perpendicular to the rod. Assume that the ball remains in contact with the rod after the collision and impulse J acts for a small time interval /_\t . Now answer the following questions: Find the impulse acted on the ball during the time /_\t

In the figure, a ball of mass m is tied with two strings of equal as shown. If the rod is rotated with angular velocity omega_(1) when