Q138 / 155 · WBJEE 2022 · Physics

The kinetic energy $\left(\mathrm{E}_{\mathrm{k}}\right)$ of a particle moving along $X$-axis varies with its position $(X)$ as shown in the figure. The force acting on the particle at $X=10 \mathrm{~m}$ is

A
$5 \hat{\mathrm{i} N}$
B
$0 \mathrm{~N}$
C
$97.5 \hat{\mathrm{i} N}$
Correct answer
D
$-5 \hat{\mathrm{i} N}$

Solution

$$ \frac{d k}{d x}=\frac{d\left(\frac{1}{2} m v^2\right)}{d x}=\frac{1}{2} m \not{2} v \frac{d v}{d x}=m a=F $$ So, Force is slope at $x=10 m \quad F=-\frac{20}{4}=-5 \hat{i}$

Hence, the correct answer is option: 'D'.

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