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Question

A car of mass m is moving on a horizontal circular track of radius r. The time taken to finish one complete revolution is π2 s. If the velocity of the car at an instant t is given by v=5sin2t, then the magnitude of tangential acceleration of the car at the time when it finishes a quarter circle is p. The value of p2 is (No slipping between the car and track)

A
6.3
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B
6.30
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C
6.2
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D
6.25
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E
6.20
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Solution

Given, v=5sin2t
dxdt=5sin2t where x is the distance covered
x0dx=t05sin2tdt
x=52cos2t..(1)
Given, time period for one complete revolution =π2s
i.e for t=π2s,x=2πr
2πr=52r=54π
So, for quarter revolution, x=πr2=58 Therefore, cos2t=14

Tangential acceleration at=dvdt=ddt(5sin2t)
at=5×2cos2t
Substituting cos2t=14
at=5×12=2.5
p=2.5
The value of p2=2.52=6.25 units

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