Out of the following pair, which one does NOT have identical dimensions is
angular momentum and Planck’s constant
impulse and momentum
moment of inertia and moment of a force
moment of inertia and moment of a force
C.
moment of inertia and moment of a force
The upper half of an inclined plane with inclination φ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by
2sinφ
2cosφ
C.
A ball is released from the top of a tower of height h metres. It takes T seconds to reach the ground. What is the position of the ball in T/3 seconds?
h/9 metres from the ground
7h/9 metres from the ground
8h/9 metres from the ground
8h/9 metres from the ground
C.
8h/9 metres from the ground
A smooth block is released at rest on a 45° incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is
A.
An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 cm. If the car is going twice as fast, i.e 120 km/h, the stopping distance will be
20 m
40 m
60 m
60 m
D.
60 m
Third equation of motion gives
v^{2} = u^{2} + 2as ⇒ 2
s ∝ u (since v = 0)
where a = retardation of body in both the cases
therefore, .... (i)
Here, s_{1} = 20 m, u1 = 60 km/h, u_{2} = 120 km/h. Putting the given values in eq. (i), we get
A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass 1/3 M and a body C of mass 2/3 M. The centre of mass of bodies B and C taken together shifts compared to that of body A towards
depends on height of breaking
does not shift
body C
body C
B.
does not shift
No horizontal external force is acting
∴ = a_{cm} =0
since v_{cm}= 0
∴∆x_{cm} = 0
A machine gun fires a bullet of mass 40 g with a velocity 1200 ms^{−1}. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
one
Four
Two
Two
D.
Two
The force exerted by machine gun on man's hand in firing a bullet = change in momentum per second on a bullet or rate of change of momentum
The force exerted by man on machine gun = 144 N Hence, number of bullets fired =144/48 = 3
A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?
3.0 cm
2.0 cm
1.5 cm
1.5 cm
D.
1.5 cm
An annular ring with inner and outer radii R_{1} and R_{2} is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, F_{1/}F_{2} is
R_{1}/R_{2}
(R_{1}/R_{2})^{2}
1
1
A.
R_{1}/R_{2}
2.0
4.0
1.6
1.6
A.
2.0
Let the mass of block be m.
Frictional force in rest position
F = mg sin 30