A particle of mass m is attached to a long ideal string. The other end of the string is joined to a vertical cylinder fixed on a frictionless horizontal plane as shown in the figure. When the particle is projected with a speed u in a direction perpendicular to the string the particle continues to move on a spiral path of decreasing radius till it strikes the cylinder. While the particle is moving on the spiral path, how will the tension in the string and speed of the particle change?

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Both will remains constant

Tension will increase and speed will remain constant

Tension will increase and speed will decrease

Both will increase

answer is D.

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Detailed Solution

Force of tension always remain perpendicular to instantaneous velocity. So work done by it is always zero and speed remains constant. But a given instant of time $T = \frac{m v^{2}}{r}$

$∵ r$ is decrease with time so T is increases

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