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A block of mass $10$ kg is placed on smooth horizontal surface. A variable force; $F = 2 t$ , where $t$ is time in second, is acting on the block at an angle $30 °$ from the horizontal. The time when block will leave the contact from the surface is ( $g = 10 m / s^{2}$ )

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$50 s$

$20 s$

$10 s$

$100 s$

answer is D.

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Detailed Solution

$F \sin 30 ° + N = 10 g$

To leave the contact, $N = 0$

or $2 t \sin 30 ° = 10 g$

or $2 t \times \frac{1}{2} = 10 \times 10$

$∴ t = 100 s$

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