A body of mass 500 g moves along x-axis such that it's velocity varies with displacement x according to the relation $\mathrm{v}=10 \sqrt{\mathrm{x}} \mathrm{m} / \mathrm{s}$ the force acting on the body is:-

JEE Main · 2023 · 11 Apr 2023 · Shift 2 · Work, Power & Energy

A body of mass 500 g moves along x-axis such that it's velocity varies with displacement x according to the relation

v = 10 x m / s

the force acting on the body is:-

(A)166 N
(B)25 N✓ Correct
(C)125 N
(D)5 N

Answer: (B)

Solution

Given

v = 10 x

, squaring gives

v^{2} = 100 x

. Differentiating with respect to x:

2 v \frac{d v}{d x} = 100

, so acceleration

a = v \frac{d v}{d x} = 50

m/s². The force is

F = ma = 0.5 \times 50 = 25

JEE Main · 2023 · 11 Apr 2023 · Shift 2 · Single correct option

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