An inclined plane makes an angle of 30° with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to

Question

An inclined plane makes an angle of 30° with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to (A) (g/3) (B) (2 g/3) (C) (5 g/7) (D) (5 g/14)

Tardigrade Admin · Accepted Answer

τ=I α α=(τ/I)=(m g r sin θ/(2)5 m r2+m r2) a=α r=(m g r2 sin θ/(2)5 m r2+m r2) a=(5 g sin 30°/7)=(5 g/14)

Q. An inclined plane makes an angle of $3 0^{\circ}$ with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to

$\frac{g}{3}$

$\frac{2 g}{3}$

$\frac{5 g}{7}$

$\frac{5 g}{14}$

$τ = I α$
$α = \frac{τ}{I} = \frac{m g r s i n θ}{\frac{2}{5} m r ^{2} + m r ^{2}}$
$a = α r = \frac{m g r ^{2} s i n θ}{\frac{2}{5} m r ^{2} + m r ^{2}}$
$a = \frac{5 g s i n 3 0 ^{\circ}}{7} = \frac{5 g}{14}$

Q. An inclined plane makes an angle of 30∘ with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to

3g​

32g​

75g​

145g​