A solid cylinder of mass m & radius R rolls down inclined plane without slipping. The speed of its C.M. when it reaches the bottom is

\(\sqrt{2gh}\)
\(\sqrt{4gh/3}\)
\(\sqrt{3/4gh}\)
\(\sqrt{4gh}\)

Solution

A raw egg and a hard boiled egg are made to spin on a table with the same angular momentum about the same axis. The ratio of the time taken by the two to stop is

= 1
< 1
> 1
None of these

Solution

A particle of mass m is moving in a plane along a circular path of radius r. Its angular momentum about the axis of rotation is L. The centripetal force acting on the particle is

L²/mr
L²m/r
L²/m r³
L² /m r²

Solution

A flywheel rotates about an axis. Due to friction at the axis,it experiences an angular retardation proportional to its angular velocity. If its angular velocity falls to half while it makes n rotations, how many more rotations will it make before coming to rest?

Solution

A particle moves in a circle of radius 0.25 m at two revolutions per second. The acceleration of the particle in metre per second² is

π²
8π²
4π²
2π²

Solution

Centripetal acceleration

a_c=4 π² v² r = 4 π² × 2 × 2 × 0.25 = 4 π² ms^-2

A body having moment of inertia about its axis of rotation equal to 3 kg-m² is rotating with angular velocity equal to 3 rad/s. Kinetic energy of this rotating body is the same as that of a body of mass 27 kg moving with a speed of

1.0 m/s
0.5 m/s
1.5 m/s
2.0 m/s

Solution

A stick of length L and mass M lies on a frictionless horizontal surface on which it is free to move in any way. A ball of mass m moving with speed v collides elastically with the stick as shown in fig.

If after the collision ball comes to rest, then what should be the mass of the ball?

m= 2 M
m = M
m = M/2
m = M/4

Solution

Two particles A and B, initially at rest, moves towards each other under a mutual force of attraction. At the instant when the speed of A is v and the speed of B is 2 v, the speed of centre of mass is

zero
v
1.5 v
3 v

Solution

What is the moment of inertia of a solid sphere of density ρ and radius R about its diameter?

\(\frac{105}{176}R^{5}\rho\)
\(\frac{105}{176}R^{2}\rho\)
\(\frac{176}{105}R^{5}\rho\)
\(\frac{176}{105}R^{2}\rho\)

Solution

A block Q of mass M is placed on a horizontal frictionless surface AB and a body P of mass m is released on its frictionless slope. As P slides by a length L on this slope of inclination θ, the block Q would slide by a distance

(m/M) L cos θ
m L/(M + m)
(M + m)/(m L cos θ)
(m L cos θ) /(m + M)

Solution

Here, the centre of mass of the system remains unchanged.in the horizontal direction. When the mass m moved forward by a distance L cos θ, let the mass(m + M) moves by a distance x in the backward direction. hence

(M + m) x – m L cos θ = 0

∴ x = (m L cos θ)/(m + M)

UnAttempted

0

Attempted

0

Correct

0

Wrong

0

Complete