Question

A solid sphere of mass $2kg$ is resting inside a cube as shown in $Fig.$. The cube is moving with a velocity $\overrightarrow{v}=(5t\hat{i}+2t\hat{j})m{s}^{-1}$. Here t is the time in seconds. All surfaces are smooth. The sphere is at rest with respect to the cube. What is the total force exerted by the sphere on the cube?

• A. $\sqrt{29}N$
• B. $29N$
• C. $26N$
• D. $\sqrt{89}N$

Answer 1

The correct option is C $26N$

$\begin{array}{c}\overrightarrow{v}=5t\hat{i}+2t\hat{j}\\ a=\left(\frac{dv}{dt}\right)=5\hat{i}+2\hat{j}\\ F=ma\\ F=m\left[a_x\hat{i}+\left(g+a_y\right)\hat{j}\right]\\ F=m\sqrt{\left({a_x}^2+{\left(g+a_y\right)}^2\right)}\\ F=2\times \sqrt{{\left(5\right)}^2+{\left(10+2\right)}^2}\\ F=2\times \sqrt{25+144}\\ F=2\times 13=26N\end{array}$

Hence,

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