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QJEEAdv22Phaff8: JEE Advanced 2022 Physics - Class 11 JEEAdv22Phaff8 Solution: A solid sphere of mass and radius rolls without slipping on a…

A solid sphere of mass 1 kg1 \mathrm{~kg} and radius 1 m1 \mathrm{~m} rolls without slipping on a fixed inclined plane with an angle of inclination θ=30∘\theta=30^{\circ} from the horizontal. Two forces of magnitude 1 N1 \mathrm{~N} each, parallel to the incline, act on the sphere, both at distance r=0.5 mr=0.5 \mathrm{~m} from the center of the sphere, as shown in the figure. The acceleration of the sphere down the plane is _________ m s−2.(m \,s^{-2} .\left(\right. Take g=10 ms−2g=10\, m s^{-2} )

JEE Advanced 2022 Paper 1 Online Physics - Rotational Motion Question 20 English

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JEE Advanced 2022 Paper 1 Online Physics - Rotational Motion Question 20 English Explanation

Taking torque about contact point.

τ⃗=mgRsin⁡30⊗+1×1⊙\vec{\tau}=m g R \sin 30^{\otimes}+1 \times 1^{\odot}

taking ⊗\otimes is positive

amp;5−1=75mR2αamp;⇒α=207rad/s2\begin{aligned}& 5-1=\frac{7}{5} m R^2 \alpha \\\\& \Rightarrow \quad \alpha=\frac{20}{7} \mathrm{rad} / \mathrm{s}^2\end{aligned}

So, acm=αR=207 m/s2a_{\mathrm{cm}}=\alpha R=\frac{20}{7} \mathrm{~m} / \mathrm{s}^2

acm=2.86 m/s2a_{\mathrm{cm}}=2.86 \mathrm{~m} / \mathrm{s}^2

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