The moment of inertia of a body about a given axis is 1.2 kgm². Initially, the body is at rest. In order to produce a rotational kinetic energy of 1500 J, an angular acceleration of 25 rad s^-2 must be applied about that axis for a duration of

4 s
2 s
8 s
10 s

Solution

Four masses are fixed on a massless rod as shown in the adjoining figure. The moment of inertia about the dotted axis is about

2 kg × m²
1 kg × m²
0.5 kg × m²
0.3 kg × m²

Solution

I = 2 × 5 × (0.2)² + 2 × 2 × (0.4)² = 1kg × m²

The wheel of a car is rotating at the rate of 1200 revolutions per minute. On pressing the accelerator for 10 seconds it starts rotating at 4500 revolutions per minute. The angular acceleration of the wheel is

30 radian /second²
1880 degrees/ second²
40 radian / second²
1980 degree/second²

Solution

If the earth is treated as a sphere of radius R and mass M,its angular momentum about the axis of its diurnal rotation with period T is

\(\frac{4\pi MR^{2}}{5T}\)
\(\frac{2\pi MR^{2}}{5T}\)
\(\frac{2\pi MR^{2}}{5T}\)
\(\frac{\pi MR^{3}}{T}\)

Solution

Angular momentum = Iω = ²⁄₅ MR².^2π⁄_T = \(\frac{4\pi MR^{2}}{5T}\)

M.I of a circular loop of radius R about the axis in figure is

MR²
(3/4) MR²
MR²/2
2MR²

Solution

Use theorem of parallel axes.

Three identical particles each of mass 1 kg are placed touching one another with their centres on a straight line.Their centres are marked A,B and C respectively. The distance of centre of mass of the system from A is

\(\frac{AB+AC+BC}{3}\)
\(\frac{AB+AC}{3}\)
\(\frac{AB+BC}{3}\)
\(\frac{AC+BC}{3}\)

Solution

A solid sphere of mass M and radius R is pulled horizontally on a sufficiently rough surface as shown in the figure.

Choose the correct alternative.

A. The acceleration of the centre of mass is F/M

B. The acceleration of the centre of mass is ²⁄₃ ^F⁄_M

C. The friction force on the sphere acts forward

D. The magnitude of the friction force is F/3

Solution

B & C are Alternatives.

A boy and a man carry a uniform rod of length L, horizontally in such a way that the boy gets 1/4^th load. If the boy is atone end of the rod,the distance of the man from the other end is