A solid sphere is rolling down in the inclined plane, from rest w… - Vidyadip

MCQ

A solid sphere is rolling down in the inclined plane, from rest without slipping. The angle of inclination with horizontal is 30°. The linear acceleration of the sphere is –

A
$28 ms ^{-2}$
B
$3.9 ms ^{-2}$
✓
$\frac{25}{7} ms ^{-2}$
D
$\frac{1}{20} ms ^{-2}$

✓

Answer

Correct option: C.

$\frac{25}{7} ms ^{-2}$

$\frac{25}{7} ms ^{-2}$
We know that, $a =\frac{g \sin \theta}{1+\frac{k^2}{ R^2}}=\frac{g \sin 30^{\circ}}{1+\frac{2}{5}}$
$\because \frac{k^2}{ R ^2} \text { for solid sphere }=\frac{2}{5} $
$a=\frac{10 \times \frac{1}{2}}{\frac{7}{5}}=\frac{25}{7}=3.6 ms ^{-2}$

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