Question

A mass of $1 \, kg$ is acted upon by a single force $\overset{ \rightarrow }{F}=\left(\right.4\hat{i}+4\hat{j}\left.\right) \, N$ . Due to force, mass is displaced from $\left(\right.0,0\left.\right)$ to $\left(1 \, m , 1 \, m\right)$ . If initially, the speed of the particle was $2 \, m \, s^{- 1}$ , its final speed should approximately be

• A. $6 \, m \, s^{- 1}$
• B. $4.5 \, m \, s^{- 1}$
• C. $8 \, m \, s^{- 1}$
• D. $7.2 \, m \, s^{- 1}$

Answer 1

Answer: (B)

Mass is displaced from (0, 0) to (1, 1). Therefore displacement is,
$\overset{ \rightarrow }{S}=\left(1 - 0\right)\hat{i}+\left(1 - 0\right)\hat{j}$
$\overset{ \rightarrow }{S}=\left(\hat{i} + \hat{j}\right) \, m$
Given force
$\overset{ \rightarrow }{F}=\left(4 \hat{i} + 4 \hat{j}\right) \, N$
$\therefore $ Work done by a constant force,
$W=\overset{ \rightarrow }{F}. \, \overset{ \rightarrow }{S}$
$W= \, \left(4 \hat{i} + 4 \hat{j}\right).\left(\hat{i} + \hat{j}\right)$
$W=4+4=8 \, J$
From work-energy theorem
$\Delta \, K=W$
$\frac{1}{2}m\left(\nu_{2}^{2} - \nu_{1}^{2}\right)=W$
$\frac{1}{2}\left(1\right)\left(\nu_{2}^{2} - 2^{2}\right)=8$
$\nu_{2}^{2}=20$
$\nu_{2}=4.5 \, m \, s^{- 1}$