A body starts rolling down on an inclined plane, the top half of which is perfectly smooth and lower half is rough. The angle of the plane being 30°, if the body is brought to rest just when it reaches the bottom, then the ratio of force of friction and weight of the body is
1 : 1
1 : 2
2 : 1
3 : 2
A particle is projected upwards from the surface of the earth (of radius R) with a KE equal to half the minimum value needed for it to escape. To what height (h) does it rise above the surface of the earth
R
2R
(R)1/2
In figure shown below, a particle is travelling counter clockwise in circle of radius 10 m. The acceleration vector indicated at a specific time. Find the value of 'v' at this time.
10 m/s
15 m/s
20 m/s
7 m/s
A lift of mass 1000 kg is descending with a speed of 6 ms-1 . Suddenly the cable of the lift begins to slip and it falls with a constant acceleration a = m / s2 . What is the kinetic energy of the lift after falling a distance 15 m ?
121.3 kJ
155.6 kJ
147.4 kJ
134.1 kJ
A solid sphere rolls without slipping and presses a spring of spring constant k as shown in figure. Then, the compression in the spring will be
D.
In case of pure rolling ratio of rotational to transitional kinetic energy is Therefore, total kinetic energy is times the transitional KE. At maximum compression, whole of kinetic energy is elastic potential. Hence,
A pendulum made of a uniform wire of cross-sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to Tm . If the Young's modulus of the material is Y, then is equal to
Work of 146 kJ is performed in order to compress one kilo mole of a gas adiabatically and in this process the temperature ofthe gas increases by 7° C. The gas is (R = 8.3 J mol-1 K-1 )
diatomic
triatomic
a mixture of monoatomic and diatomic
monoatomic
Which of the following graphs represents resonance for low damping ?
graph (1)
graph (2)
graph (3)
None of these
A bat emitting an ultrasonic wave of frequency 2 x 104 Hz flies at a speed of 6 m/s between two parallel walls. The beat frequency between the two frequencies heard
by the bat is (Given, speed of sound is 330 m/s)
600 Hz
800 Hz
900 Hz
1300 Hz
Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases to Vq , where V is the volume of the gas. The value of q is