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A solid sphere of mass 2 kg is resting inside a cube as shown in the figure. The cube is moving with a velocity $\vec{V} = (5 \hat{i} + 2 t \hat{j}) m / s$ . Here t is the time in second. 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 ? (Take g = 10 $m / s^{2}$ )

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$\sqrt{29} N$

24 N

26 N

$\sqrt{89} N$

answer is B.

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Detailed Solution

$As \vec{v} = 5 \hat{i} + 2 t \hat{j} ∴ \vec{a} = a_{x} \hat{i} + a_{y} \hat{j} = + 2 \hat{j}$

$\vec{F} = m a_{x} \hat{i} + m (g + a_{y}) \hat{j}$

$∴ | \vec{F} | = m \sqrt{a_{x}^{2} + {(g + a_{y})}^{2}} = 24 N$

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