At any instant the velocity of a particle of mass 500 g is If the force acting on the particle at = 1 s is then the value of will be [2023]

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Solution

Q.
At any instant the velocity of a particle of mass 500 g is $(2 t \hat{i} + 3 t^{2} \hat{j}) {m s}^{- 1} .$ If the force acting on the particle at $t$ = 1 s is $(\hat{i} + x \hat{j}) N,$ then the value of $x$ will be [2023]

1 3

2 6

3 2

4 4

Ans.
(1)

$\vec{v} = 2 t \hat{i} + 3 t^{2} \hat{j}$

$\vec{a} = 2 \hat{i} + 6 t \hat{j}$

$At t = 1, \vec{a} = 2 \hat{i} + 6 \hat{j}$

$\vec{F} = m \vec{a} = 0.5 (2 \hat{i} + 6 \hat{j}) = \hat{i} + 3 \hat{j}$

$\vec{F} = \hat{i} + x \hat{j}$

Hence $x$ = 3

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