A body of mass 500 g moves along the -axis such that its velocity varies with displacement according to the relation m/s. The force acting on the body is [2023]

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Solution

Q.
A body of mass 500 g moves along the $x$ -axis such that its velocity varies with displacement $x$ according to the relation $v = 10 \sqrt{x}$ m/s. The force acting on the body is [2023]

1 166 N

2 25 N

3 125 N

4 5 N

Ans.
(2)

$v = 10 \sqrt{x} \Rightarrow v^{2} = 100 x$

$2 v \frac{d v}{d x} = 100 \Rightarrow a = 50 {m/s}^{2}$

$Hence, F = 25 N$

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