An object with mass 500 g moves along x -axis with speed $\mathrm{v}=4 \sqrt{\mathrm{x}} \mathrm{m} / \mathrm{s}$. The force acting on the object is :

JEE Main · 2025 · 07 Apr 2025 · Shift 2 · Laws of Motion

An object with mass 500 g moves along x -axis with speed

v = 4 x m / s

. The force acting on the object is :

(A)8 N
(B)5 N
(C)6 N
(D)4 N✓ Correct

Answer: (D)

Solution

With

v = 4 x

, squaring gives

v^{2} = 16 x

. Differentiating with respect to position,

2 v \frac{d v}{d x} = 16

, so the acceleration is

a = v \frac{d v}{d x} = 8 m/s^{2}

. For a mass of

0.5 kg

, the force is

F = ma = 0.5 \times 8 = 4 N

JEE Main · 2025 · 07 Apr 2025 · Shift 2 · Single correct option

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