A sphere of mass
Question:

A sphere of mass $2 \mathrm{~kg}$ and radius $0.5 \mathrm{~m}$ is rolling with an initial speed of $1 \mathrm{~ms}^{-1}$ goes up an inclined plane which makes an angle of $30^{\circ}$ with the horizontal plane, without slipping. How low will the sphere take to return to the starting point $\mathrm{A}$ ?

  1. $0.60 \mathrm{~s}$

  2. $0.52 \mathrm{~s}$

  3. $0.57 \mathrm{~s}$

  4. $0.80 \mathrm{~s}$


Correct Option: , 3

Solution:

(3) $\mathrm{a}=\frac{\mathrm{g} \sin \theta}{1+\frac{\mathrm{I}}{\mathrm{mR}^{2}}}=\frac{5}{7} \times \frac{10}{2}=\frac{25}{7}$

$\mathrm{t}=\frac{2 \mathrm{v}_{0}}{\mathrm{a}}=\frac{2 \times 1 \times 7}{25}$

$=0.56$

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