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Q.

A solid sphere of mass 1 kg and radius 1 m rolls without slipping on a fixed inclined plane with an angle of inclination 𝜃 = 30° from the horizontal. Two forces of magnitude 1 N each, parallel to the incline, act on the sphere, both at distance 𝑟 = 0.5 m from the center of the sphere, as shown in the figure. The acceleration of the sphere down the plane is ____ 𝑚𝑠 ^-2. (Take 𝑔 = 10 𝑚𝑠^-2 .)

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answer is 2.86.

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Detailed Solution

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Taking torque about contact point.
$\vec{τ} = m g R \sin 30^{\otimes} + 1 \times 1^{⊙}$
$taking \otimes is positive$
$\begin{array}{l} 5 - 1 = \frac{7}{5} m R^{2} α \\ \Rightarrow α = \frac{20}{7} rad / s^{2} \\ So, a_{cm} = α R = \frac{20}{7} m / s^{2} \\ a_{cm} = 2.86 m / s^{2} \end{array}$

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A solid sphere of mass 1 kg and radius 1 m rolls without slipping on a fixed inclined plane with an angle of inclination = 30° from the horizontal. Two forces of magnitude 1 N each, parallel to the incline, act on the sphere, both at distance = 0.5 m from the center of the sphere, as shown in the figure. The acceleration of the sphere down the plane is ____ -2. (Take = 10 -2 .)