Question

A steel ball of mass $5$ $g$ is thrown downward with velocity $10$ ${ms}^{-1}$ from height $19.5$ $m$ . It penetrates sand by $50$ $cm$ . The change in mechanical energy will be ( $g=10$ ${ms}^{-2}$ )

• A. $1$ $J$
• B. $1.25$ $J$
• C. $1.5$ $J$
• D. $1.75$ $J$

Answer 1

The correct option is B $1.25$ $J$

$\begin{array}{c}Thechangeinmechanicenergy\Delta U=mg\left(h+x\right)+\frac{1}{2}m{v}^2\\ herem=5g=0.005kg\cdot h=19.5mx=50cm=0.5m,v=10m/s\\ So,\Delta U=0.005\times 10919.5+0.5+\frac{1}{2}\times 0.005\times {\left(10\right)}^2=0.005\times 10\times 20+\frac{1}{2}\times 0.005\times 100=1.25J\end{array}$

Hence,

option $\left(B\right)$ is correct answer.