Four particles of mass m 1
= 2m, m 2 = 4m, m 3 = m
and m 4 are placed at four
corners of a square. What
should be the value of m 4
so that the centre of mass
of all the four particles are
exactly at the centre of the
square?
(a) 2 m (b) 8 m
(c) 6 m (d) None of these
For the same total mass, which of the following
will have the largest moment of inertia about an
axis passing through the centre of gravity and
perpendicular to the plane of body?
(a) A ring of radius l
(b) A disc of radius l
(c) A square lamina of side 2l
(d) Four rods forming square of side 2l
A ring rolls down, starting from rest, down an
inclined plane of length l and inclination q. e
velocity of the centre of mass of the ring at the mid
point of the inclined plane is
(a) glsinθ (b) glsinT
2
(c) 2 glsinT (d)^4
7
glsinT
If a disc slides from top to bottom of an inclined
plane, it takes time t 1. If it rolls, it takes time t 2. Now,
t
t
2
2
1
2 is
(a)^1
2
(b)^2
3
(c)^3
2
(d)
2
5
A wheel is rolling straight on
ground without slipping. If the
axis of the wheel has speed v, the
instantaneous velocity of a point
P on the rim, de ned by angle q,
relative to the ground will be
(a) v cos q/2 (b) 2v cos q/
(c) v (1 + sin q) (d) v (1 + cos q).
m 1
m 4
m 2
m 3
P q
A uniform rod of length l is free to
rotate in a vertical plane about a
fixed horizontal axis through its
centre. The rod begins rotation from
rest from its unstable equilibrium
position. When it has turned
through an angle q, its angular
velocity Z is given as
(a)^6 g
l
sin q (b)^6
2
g
l
sin
T
(c)^6
2
g
l
cos
T (d) 6 g
l
cos q
A wheel of radius r and mass m stands in front of
a step of height h. The least horizontal force which
should be applied to the axle of the wheel to allow
it to raise on to the step is
(a) mghrh
rh
()2
(b) mgh (r – h)
(c)
mg hrh
rh
() 2
(d) none of these
A ball weighing 15 g is tied to a string 10 cm long.
Initially the ball is held in
position such that the string
is horizontal. The ball is now
released. A nail N is situated
vertically below the support
at a distance L. The minimum
value of L such that the string
will be wound round the nail is
(a) 2 cm (b) 4 cm (c) 6 cm (d) 8 cm
If the density of the material of a square plate and
a circular plate shown in the figure is the same, the
center of mass of the composite
system will be
(a) inside the square plate
(b) inside the circular plate
(c) at the point of contact
(d) outside the system
Two blocks of equal mass are tied with a light string
which passes over a massless pulley as shown in the
gure.
