An object with mass 500 g moves along x -axis with speed $v=4 \sqrt{x} \mathrm{~m} / \mathrm{s}$. The force…

An object with mass 500 g moves along x -axis with speed $v=4 \sqrt{x} \mathrm{~m} / \mathrm{s}$. The force acting on the object is :
  1. 8 N
  2. 5 N
  3. 6 N
  4. 4 N

Solution

$\begin{aligned} & F=M \times a \\ & v=4 \sqrt{x} \\ & v^2=16 x \\ & 2 v \frac{d v}{d x}=16 \\ & \frac{v d v}{d x}=\frac{16}{2}=8 \\ & F=0.5 \times 8=4 N\end{aligned}$

Asked in: JEE Main 2025 (07 Apr Shift 2)

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