Question

A particle of mass $20\text{g}$ is thrown vertically upwards with a speed of $10\text{m/s}$. Find the work done by the gravity during the time of ascent of the particle.

• A. $1\text{J}$
• B. $-1\text{J}$
• C. $2\text{J}$
• D. $-2\text{J}$

Answer 1

The correct option is B $-1\text{J}$

Suppose the particle reaches the maximum height ${}^{\prime }{h}^{\prime }$. Since the velocity at the highest point is zero, on applying kinematic equation
$v^2=u^2+2as$
$(\because v=0)$
$0=u^2-2gh$
$h=\frac{u^2}{2g}$
The work done by gravity is equal to,
$W_{\text{gravity}}=-mgh=mg\left(\frac{u^2}{2g}\right)$
$W_{\text{gravity}}=-\frac{1}{2}m{u}^2$
$\therefore W_{\text{gravity}}=-\frac{1}{2}\times \frac{20}{1000}\times (10{)}^2=-1\text{J}$