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The moment of inertia, the radius of gyration, values of moments of inertia for simple geometrical objects Short Tricks for JEE

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Short tricks for The moment of inertia, the radius of gyration, values of moments of inertia for simple geometrical objects work only with strong fundamentals. Apply the tips below in timed sets and review every explanation.

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  • Dimensional check first

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  • Limiting cases

    Substitute extreme values (t→0, m→∞, θ→0) to sanity-check your final expression.

Syllabus context

Part of Rotational Motion in JEE Main Physics.

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Q1PhysicsUnit 5: Rotational Motion
Two point size bodies of masses 20g20 g 30g30 g are fixed at two ends of a light rod of length 1.5m.1.5 m . The moment of inertia of these two bodies about an axis perpendicular to the length of rod and passing through their center of mass is:
Q2PhysicsUnit 5: Rotational Motion
Two solid spheres AA and BB each of radius ′R′^{\prime} R^{\prime} are made of materials of densities ρA\rho_{A} and ρB\rho_{B} respectively. Their moments of inertia about a diameter are⁡IA\operatorname{are} I_{A} and IBI_{B} respectively. The value of IAIB\frac{\boldsymbol{I}_{A}}{\boldsymbol{I}_{B}} is:
Q3PhysicsUnit 5: Rotational Motion
In which of the following cases of rolling body, translatory and rotational kinetic energies are equal
Q4PhysicsUnit 5: Rotational Motion
The ratio of moments of inertia of two solid spheres of same mass but densities in the ratio 1: 8 is:
Q5PhysicsUnit 5: Rotational Motion
The twisting couple per unit twist for a solid cylinder of radius 4.9cm4.9 \mathrm{cm} is 0.1N/m.0.1 N / m . The twisting couple per unit twist for a hollow cylinder of same material with outer and inner radii of 5cm5 \mathrm{cm} and 4cm4 \mathrm{cm} respectively, will be
Q6PhysicsUnit 5: Rotational Motion
In a rectangle ABCD(BC=2AB)A B C D(B C=2 A B) the moment of inertia along axis will be minimum through:
Q7PhysicsUnit 5: Rotational Motion
The radius of gyration of a disc of mass 100g100 g and radius 5cm5 c m about an axis passing through its centre of gravity and perpendicular to the plane is (in cm\mathrm{cm}
Q8PhysicsUnit 5: Rotational Motion
An object is allowed to roll down an inclined plane starting from rest (consider the object to be uniform and having same mass) then object having largest rotational momentum is (if rotated with same angular momentum)

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