Question

A truck and a car are running at same velocity. If the mass of truck is $10times$ that of car , the ratio of kinetic energy of truck and car is:

• A. $1:10$
• B. $2:5$
• C. $10:1$
• D. $5:2$

Answer 1

The correct option is C

$10:1$

Step 1: Given data

Mass, $m_{truck}=10\times m_{car}$

velocity, $v_{truck}=v_{car}$

Ratio of kinetic energy of truck and car, $\frac{K.E{.}_{truck}}{K.E{.}_{car}}=?$ (To be calculated)

Step 2: Formula for kinetic energy:

$$\begin{gathered} K.E.=\frac{1}{2}\times m\times v^2 \\ \therefore v=\sqrt{\frac{2\times K.E.}{m}} \end{gathered}$$

where,

$$\begin{gathered} K.E.=KineticEnergy \\ m=mass \\ v=velocity \end{gathered}$$

Step 3: By putting the values in the above expression, we get

$$\begin{gathered} v_{truck}=v_{car} \\ \Rightarrow \sqrt{\frac{2\times K.E{.}_{truck}}{m_{truck}}}=\sqrt{\frac{2\times K.E{.}_{car}}{m_{car}}} \\ \Rightarrow \frac{K.E{.}_{truck}}{K.E{.}_{car}}=\frac{m_{truck}}{m_{car}} \\ \Rightarrow \frac{K.E{.}_{truck}}{K.E{.}_{car}}=\frac{10\times m_{car}}{m_{car}} \\ \Rightarrow \frac{K.E{.}_{truck}}{K.E{.}_{car}}=\frac{10}{1} \end{gathered}$$

Hence, the correct answer is option (C).