CBSE Class 11 Physics Worksheet Set 04 Solved

1. State the theorem of perpendicular axes for moment of inertia. 

2. Particle of mass 0.2Kg is moving in a circle of radius 1m with frequency 2/π S^-1 . Find its angular momentum.

3. Why is it more difficult to revolve a stone tied to a large string than a stone tied to a smaller string?

4. Which physical quantity is represented by the product of moment of inertia and angular velocity? 

5. Standing is not allowed in double decker bus. Why? 

6. Three identical spheres each of radius R, placed touching each other on a horizontal table. Locate the position of the centre of mass of the system.

7. Define radius of gyration. Write its SI unit and dimensional formula. 

8. Derive the relation between torque and angular momentum. 

9. If the earth were suddenly contract to half of its present size, by how much would the day be decreased? Given moment of inertia of the earth = 2/5 MR².

10.Derive an expression of centre of mass of a two particles system. 

11.Derive an expression for the rotational kinetic energy of a body. State the factors on which rotational kinetic energy of a body depends.

VALUE POINTS 

1. The moment of inertia of a plane lamina about an axis perpendicular to its plane is equal to the sum of the moments of inertia of the lamina about any two mutually perpendicular axes in its plane and intersecting each other at the point where the perpendicular axis passes though it.

2. w = 4 rad s^-1, v = rw =4 X 1 = 4ms^-1, L = mvr L = 0.8Kgm2s^-1

3. Moment of inertia of a stone tied to longer string is more than the moment of inertia of a stone tied to a smaller string.

4. Angular momentum(L) 

5. A body is said to be more stable when its CENTER OF GRAVITY is kept as low as possible. In a double decker bus, the c.g. of our body is obviously at higher place than the lower deck.In addition, if we stand the c.g. goes the higher, which will lead for a great imbalance to be followed by a severe fall off.

6. r= m₁r₁ +m₂r₂+ m₃r₃ / m₁+m₂+m₃

r= (0,0) + (2R,0) + (R,√3 R) / 3

r = (R , R/√3)

7. Definition
SI Unit is metre.
(M ⁰L¹T ⁰)

8. Derivation: τ = d L/dt, 

9. from the principle of conservation of angular momentum
I´ω´＝Iω
T¹ = 6hr
Day will be decreased by (24hr – 6hr) = 18hr

10. Derivation : R _cm = (m₁r₁ + m₂r₂ ) / (m₁ + m₂) 

11. E_k = ½ Iw²
Rotational kinetic energy depends on the factors:
(i) Moment of inertia (ii) angular speed of the body.

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