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A small ball is connected to a block by a light string of length $l$ . Both are initially on the ground. There is sufficient friction on the ground to prevent the block from slipping. The ball is projected vertically up with a velocity is, where $2 g l < u^{2} < 3 g l .$ The center of mass of the block $+$ ball system is $C .$

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$C$ will move along a circle

$C$ will move along a parabola

$C$ will move along a straight line

The horizontal component of the velocity of the ball will first increase and then decrease

answer is A, D.

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Detailed Solution

As the block does not move the ball moves along a circle. The center of mass of the system lies some where on the string. Thus

$\frac{1}{2} m v^{2} + m g l \sin θ = \frac{1}{2} m u^{2} v_{H} = v \sin θ = \sin θ \sqrt{u^{2} - 2 g l \sin θ}$

For $m a x^{m} v_{H}, \frac{d v_{T}}{d θ} = 0,$ which gives $\sin θ = \frac{u^{2}}{3 g l}$

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