Question


A cart of mass has a pole on it from which a ball of mass  hangs from a thin string attached to point P. The cart and the ball have initial velocity . The cart crashes onto another cart of mass and sticks to it. The length of the string is . If the smallest initial velocity from which the ball can go in the circle around point P is , find the value of . (Neglect friction and take , )

43073
expand
A

B

C

D

Hard

Solution

verified
Verified by Toppr
Correct option is C)

m, M 

Momentum conservation gives:

velocity of the two carts after collision

Consider the circular motion of the ball atop the cart if it were stationery. If at the lowest and highest points the ball has speeds  and , respectively, then



and ,

where is the tension in the string when the ball is at the highest point.

The smallest  is given by .

The smallest  is given by





When the cart is moving, is the velocity of the ball relative to the cart. As the ball has initial velocity, velocity of the ball relative to the cart after the collision is . Hence, the smallest velocity for the ball to go round in a circle after the collision is given by:




Video Explanation

Solution To Question ID 43073
play-icon

Was this answer helpful?

upvote 0
downvote0

Similar questionsstar-struck

There are small elastic balls placed at rest on a smooth horizontal surface which is circular of radius, at other end. The masses of balls are , , , ......., , respectively. The least velocity which should be provided to the first ball of mass, , such that ball completed vertical circle is

135328
expand
View solution
>

A ball of mass 0.6kg attached to a light inextensible string rotates in a vertical circle of radius 0.75m such that it has speed of 5 m/s when the string is horizontal. Tension in string when it is horizontal on other side is:

View solution
>

If a particle is projected with speed, , from ground at an angle, , with horizontal, then radius of curvature of a point where velocity vector is perpendicular to initial velocity vector is given by:

View solution
>

A ball of mass is attached to the end of a string having length The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is The maximum possible value of angular velocity of ball (in ) is:

28714
expand
View solution
>

A mass is attached to one end of a mass less string (length ), the other end of which is attached to a fixed support O. The mass swings around in a vertical circle as shown in fig. The mass has the minimum speed (u = necessary at the lowermost point of the circle to keep the string from going slack. If you cut the string, when it is making angle (as shown in figure) with vertical line through centre O of the circle, the resulting projectile motion of the mass has its maximum height located directly above the center of the circle.

Find the value of

131046
expand
View solution
>

View more