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 , )







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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:

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Solution To Question ID 43073

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