Question

A sphere of mass $1kg$ rests at one corner of a cube. The cube is moved with a velocity $\overrightarrow{v}=8t\hat{i}-2t^2\hat{j}.$ Where $t$ is time in second. The force by sphere on the cube at $t=1$ is ($g=10m{s}^{-2}$) [Figure shows vertical plane of the cube]:

• A. $8N$
• B. $10N$
• C. $20N$
• D. $4\sqrt{5}N$

Answer 1

The correct option is D $4\sqrt{5}N$

Given the cube is moving with a velocity of

$\overrightarrow{v}=8t\hat{i}-2t^2\hat{j}$

Acceleration of the cube will be

$dv/dt=8\hat{i}-4t\hat{j}$

acceleration at time $t=1$ is

$8\hat{i}-4\hat{j}$

The pseudo force on the sphere will be $-mdv/dt$

Where $m$ is the mass of the sphere

$=-8\hat{i}+4\hat{j}$

So the magnitude of force is $\sqrt{64+16}$

$=\sqrt{80}=4\sqrt{5}$ N