At any instant the velocity of a particle of mass 500 g is (2ti + 3t²j) m s⁻¹. If the force acting on the particle at t = 1 s is (i + xj) N. Then the value of x will be: (a) 2 (b) 4 (c) 6 (d) 3

Answer: (d). a = dv/dt = 2i + 6tj; at t = 1 s, a = 2i + 6j F = ma = 0.5(2i + 6j) = i + 3j N So x = 3. The answer is (d) 3.

At any instant the velocity of a particle of mass 500 g is (2ti +… | JEE Main 2023 (8 Apr, Shift 1)

Q17JEE Main 2023 · 8 APR · SHIFT 1Medium

Inertia, First & Second Laws

At any instant the velocity of a particle of mass $500\text{ g}$ is $\left(2t\hat{i} + 3t^2\hat{j}\right)\text{ m s}^{-1}$ . If the force acting on the particle at $t = 1\text{ s}$ is $(\hat{i} + x\hat{j})\text{ N}$ . Then the value of $x$ will be:

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Answer: (d)

$\vec{a} = \frac{d\vec{v}}{dt} = 2\hat{i} + 6t\hat{j}$ ; at $t = 1$ s, $\vec{a} = 2\hat{i} + 6\hat{j}$
$\vec{F} = m\vec{a} = 0.5(2\hat{i} + 6\hat{j}) = \hat{i} + 3\hat{j}\text{ N}$
So $x = 3$ . The answer is (d) 3.

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