(a)()MmgMmI
r−
++
2
2(b)()MmgMmI
r−
+−
2
2(c)()MmgMmI
r−
++
(^2)
(d)
()Mmg
Mm
I
r−
+−
(^2)
- Two uniform boards, tied
together with the help
of a string, are balanced
on a surface as shown in
gure.
e coecient of static
friction between boards and surface is 0.5. e
minimum value of q, for which this type of
arrangement is possible is
(a) 30°
(b) 45°
(c) 37°
(d) It is not possible to have this type of balanced
arrangement. - A solid cylinder is placed on the end of an inclined
plane. It is found that the plane can be tipped at an
angle q before the cylinder starts to slide. When the
cylinder turns on its sides and is allowed to roll, it is
found that the steepest angle at which the cylinder
performs pure rolling is φ. e ratio of tan φ/tan q is
(a) 3 (b) 1/3 (c) 1 (d) 1/2 - In the gure shown mass of
both, the spherical body and
block is m. Moment of inertia
of the spherical body about
centre of mass is 2mR^2. e
spherical body rolls on the
horizontal surface. ere is
no slipping at any surfaces in contact. e ratio of
kinetic energy of the spherical body to that of block is
(a) 3/4 (b) 1/3 (c) 2/3 (d) 1/2
More than one Options Correct Type - e moments of inertia of
a thin square plate ABCD
of uniform thickness
about an axis passing
through the centre O and
perpendicular to the plate
are
q qR2 R4 B 13
2
D COA(a) I 1 + I 2 (b) I 3 + I 4
(c) I 1 + I 3 (d) I 1 + I 2 + I 3 + I 4
(Where I 1 , I 2 , I 3 and I 4 are respectively, the moments
of inertia about axes 1, 2, 3 and 4, where axes are in
the plane of the plate).- A wheel is rolling on a horizontal plane. At a certain
instant, it has a velocity ‘v’ and acceleration ‘a’ of
CM as shown in gure. Acceleration of
(a) A is vertically upwards
(b) B may be vertically
downwards
(c) C cannot be horizontal
(d) some point on the
rim may be horizontal
le wards - A particle of mass m is projected with a velocity
v making an angle of 45° with the horizontal.
e magnitude of the angular momentum of the
projectile about the point of projection, when the
particle is at its maximum height h, is
(a) zero (b)mv
g342(c)mv
g32(d) mg 2 h^3- e torque
τ on a body about a given point is
found to be equal to
ALand where
A is a constant
vector, and
L is the angular momentum of the body
about that point. From this it follows that(a) dL
dt
is perpendicular to
L at all instants of time(b) the component of
L in the direction of A does
not change with time.
(c) the magnitude of
L does not change with time.
(d)
Ldoes not change with time.Numerical Value Type- One fourth length of a uniform rod of length 2l and
mass m is placed on a horizontal table and the rod
is held horizontal. e rod is released from rest. e
normal reaction on the rod as soon as the rod is
released is xmg
31
. Find the value of x.
2 l
1/4Oa
vBAC