2018-10-01_Physics_For_You

60° 30°

The magnitude of acceleration of centre of mass of
both blocks is (neglect friction everywhere)

(a)^31

42

 









g^ (b)

31

42

 









g

(c)^31

22

 −







g^ (d)

31

22

 









g

11. Two steel balls of equal diameter are connected by
    a rigid bar of negligible weight as shown and are
    dropped in the horizontal position from height h
    above the heavy steel and brass base plates. If the
    coefficient of restitution between the ball and steel
    base is 0.6 and that between the other ball and the
    brass base is 0.4. The angular velocity of the bar
    immediately after rebound is (Assume the two
    impacts are simultaneous).

Steel

l = 1 m

h = 0.2 m

Brass

(a)

2

5

rad s−^1 (b)^1

5

rad s−^1

(c)

3

5

rad s−^1 (d)^1

4

rad s−^1

12. A uniform rod of mass m and length l 0 is rotating
    with a constant angular speed Z about a vertical axis
    passing through its point of suspension. The moment
    of inertia of the rod about the axis of rotation if it
    makes an angle q to the vertical (axis of rotation) is

(a)

ml 022

12

sin T

(b)

ml 022

6

sin T

(c)

2

3

0

ml^22 sin T

(d)

ml 022

3

sin T

13. A rod of mass m is placed on
    smooth table. For what value of
    x, the point P on the rod of length
    l = 6 m has zero acceleration if a
    force F is applied at the end of rod
    as shown in gure.
    (a) 1 m (b) 2 m
    (c) 2.5 m (d) 1.5 m

F

C

P

x

14. A rod of mass m is placed on a solid and hollow
    spheres each of mass m. If the speed of the plate
    is v, assuming pure rolling of the spheres with all
    contacting surfaces, the kinetic energy of the system
    (spheres + plate) will be
    m v
    v/2 v/

(a)

43

50

mv^2 (b)^33

50

mv^2 (c)^43

60

mv^2 (d)^53

60

mv^2

15. The angular momentum
    of the disc which spins

with ω=^3 v

R

k and its

CM moves with a

velocity

 

vv= i about O

will be

(a)^3

2

mvRk (b) mvRk

2



(c) −^3

2

mvR

k^ (d) −

mvR

k

2



16. A cotton reel rolls
    without sliding such
    that the point P of the
    string has velocity
    v = 6 m s–1. If r = 10
    cm and R = 20 cm,
    then the velocity of
    its centre C is
    (a) 2.5 m s–1 (b) 5 m s–
    (c) 4 m s–1 (d) 2 m s–


17. A homogenous rod of length l = Kx and mass M
    is lying on a smooth horizontal floor. A bullet of
    mass m hits the rod at a distance x from the middle
    of the rod at a velocity v 0 perpendicular to the rod
    and comes to rest aer collision. If the velocity of
    the farther end of the rod just aer the impact is in
    the opposite direction of v 0 , then
    (a) K > 3 (b) K < 3 (c) K > 6 (d) K < 6


18. A uniform rod of length L and mass M is held
    vertical, with its bottom end pivoted to the floor.
    The rod falls under gravity, freely turning about
    the pivot. If acceleration due to gravity is g, what is
    the instantaneous angular speed of the rod when it
    makes an angle 60° with the vertical

v

m

x

y

R

O

disc

^3 v

R

C R

P

v = 6 m s–

r