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
R_{2}/R_{1}
A.
R_{1}/R_{2}
A projectile can have the same range R for two angles of projection. If t_{1} and t_{2} be the times of flights in the two cases, then the product of the two time of flights is proportional to
R^{2}
1/R^{2}
1/R
R
D.
R
A particle is moving eastwards with a velocity of 5 m/s in 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is
zero
D.
towards north-westThe 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
tanφ
C.
A car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance traversed is 15 S, then
S=ft
S= ft^{2}/72
S = 1/2 ft^{2}
S = 1/4 ft^{2}
B.
S= ft^{2}/72
The relation between time t and distance x is t=ax^{2} +bx where a and b are constants. The acceleration is
−2abv^{2}
2bv^{3}
−2av^{3}
2av^{2}
C.
−2av^{3}
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
work and torque
C.
moment of inertia and moment of a force
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
1.0 cm
D.
1.0 cm
A parachutist after bailing outfalls 50 m without friction. When a parachute opens, it decelerates at 2 m/s^{2}. He reaches the ground with a speed of 3 m/s. At what height, did he bail out?
91 m
182 m
293 m
111 m
C.
293 m
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.
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