JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Work, Power & Energy

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A body of mass 2 kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P. Its displacement in 4 s is

\frac{1}{3} α^{2} P

m. The value of

α

will be ......

Answer: 4

Solution

Under constant power the work--energy theorem gives

\frac{1}{2} m v^{2} = P t

, so

v = \frac{2 P t}{m}

. Integrating the displacement,

x = \int_{0}^{4} \frac{2 P}{m} t^{1/2} d t = \frac{2 P}{m} \cdot \frac{2}{3} t^{3/2}_{0}^{4}

, and with

m = 2

kg and

4^{3/2} = 8

this becomes

x = P \times \frac{2}{3} \times 8 = \frac{16}{3} P

. Comparing with

\frac{1}{3} α^{2} P

gives

α^{2} = 16

, so

α = 4

JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Integer answer

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