A particle of mass m is driven by a machine that delivers a constant power k watts

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A particle of mass m is driven by a machine that delivers a constant power k watts.If the particle starts from rest the force on the particle at time t is

Options

(a) √(mk/2) t⁻¹/²
(b) √(mk) t⁻¹/²
(c) √2mk t⁻¹/²
(d) 1/2√(mk) t⁻¹/²

Correct Answer:

√(mk/2) t⁻¹/²

Explanation:

As we know power P = dw / dt
w = Pt = (1/2) mV²
So, v = √(2Pt / m)
Hence, acceleration a = dV / dt = √(2P / m).(1/2√t)
Therefore, force on the particle time ‘t’ = ma
= √(2Km² / m) . (1/2√t) = √(Km / 2t) = √(mK / 2) t⁻¹/₂

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Topics: Work Energy and Power (94)
Subject: Physics (2479)

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