Question

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

• 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

$\begin{array}{c}Takingthepotentialenergytobezeroatthefinallevelwheretheparticlereachesafter\\ penetrationinthesand.\\ Totalmechanicalenergy\\ kineticenergy=\frac{1}{2}\times \frac{5}{1000}\times {10}^2=\frac{1}{2}\times \frac{5}{1000}\times 100=\frac{1}{4}J\\ potentialenergy=\frac{5}{1000}\times 10\times \left(19.5+0.5\right)=1J\\ totalmechanicalenergy=1+\frac{1}{4}=\frac{5}{4}=1.25J\end{array}$

Hence,

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