Moment of inertia about an axis AB for a rod of mass 40 kg and length 3 m is same as that of a solid sphere of mass 10 kg

Question

Moment of inertia about an axis AB for a rod of mass 40 kg and length 3 m is same as that of a solid sphere of mass 10 kg and radius R about an axis parallel to AB axis with separation of 3 m as shown in figure below. The value of R is given as $\sqrt{\frac{α}{2}}$ . The value of $α$ is _______. [2026]

Smart Achievers · Accepted Answer

(15)

$Moment of inertia about an axis A B for a rod is same as that of a solid sphere, I_{Rod} = I_{SS}$

$\frac{M_{1} L^{2}}{3} = (\frac{2}{5} m_{2} R^{2} + m_{2} L^{2})$

$\frac{40 \times {(3)}^{2}}{3} = \frac{2}{5} \times 10 \times R^{2} + 10 \times {(3)}^{2}$

$120 = 4 R^{2} + 90$

$4 R^{2} = 30$

$R = \sqrt{\frac{15}{2}} = \sqrt{\frac{α}{2}} \Rightarrow α = 15$

Solution

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Solution

Q. Moment of inertia about an axis AB for a rod of mass 40 kg and length 3 m is same as that of a solid sphere of mass 10 kg and radius R about an axis parallel to AB axis with separation of 3 m as shown in figure below. The value of R is given as α2. The value of α is _______. [2026]

Ans. (15) Moment of inertia about an axis AB for a rod is same as that of a solid sphere, IRod=ISS M1L23=(25m2R2+m2L2) 40×(3)23=25×10×R2+10×(3)2 120=4R2+90 4R2=30 R=152=α2⇒α=15

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