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  • A particle of mass 10 g moves in a straight line with retardation 2x, where x is the displacement in SI units. Its loss of kinetic energy for above displacement is <img alt="\left ( \fr

A particle of mass 10 g moves in a straight line with retardation 2x, where x is the displacement in SI units. Its
loss of kinetic energy for above displacement is \left ( \frac{10}{x} \right )^{-n}. The value of n will be ____________

Option: 1

2


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\begin{aligned} & \text { Given, } a=-2 x \\ & \Rightarrow \frac{v d v}{d x}=-2 x \\ & \Rightarrow v d v=-2 x d x \\ & \Rightarrow \int_{v_1}^{v_2} v d v=-2 \int_0^x x d x \\ & \Rightarrow \frac{v_2^2}{2}-\frac{v_1^2}{2}=-\frac{2 x^2}{2} \\ & \Rightarrow \frac{m v_1^2}{2}-\frac{m v_2^2}{2}=m x^2=\frac{10}{1000} x^2=10^{-2} x^2=\left(\frac{10}{x}\right)^{-2} \\ & \mathrm{n}=2 . \end{aligned}

Posted by

Pankaj Sanodiya

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