Question

A small object of mass of $100\,\text{g}$ moves in a circular path. At a given instant velocity of the object is $10\hat{i}\,ms^{- 1}$ and acceleration is $\left(\right.20\hat{i}+10\hat{j}\left.\right)\,ms^{- 2}$ . At this instant of time, the rate of change of kinetic energy of the object is (in SI units)

• A. $200 \, kgm^{2}s^{- 2}$
• B. $300\,kgm^{2}s^{- 2}$
• C. $10000\,kgm^{2}s^{- 2}$
• D. 20

Answer 1

Answer: (D)

Given, the mass of the object $\left(m\right)=100 \, g$
$=100\times 10^{- 3} \, kg$
Velocity of object $\left(v\right)=10\hat{i} \, m \, s^{- 1} \, $
Acceleration of object $\left(a\right)=\left(\right.20\hat{i}+10\hat{j}\left.\right) \, m \, s^{- 2}$
We know that,
$\frac{d \left(\right. K E \left.\right)}{d t}=F.v=ma.v \, \, \left[\right. \because K . E . = \frac{1}{2} m v^{2} \left]\right.$
$=\left(\right.100\times \left(10\right)^{- 3}\left.\right)\left(\right.20\hat{i}+10\hat{j}).\left(\right.10\hat{i}\left.\right)$
$=100\times 10^{- 3}\times 200$
$=\frac{100 \times 200}{1000}=20 \, kg \, m^{2 \, }s^{- 3} \, $