ball of mass (m) 0.5 kg is attached to the end of a string having a length (L) 0.5 m. The ball is rotated on a horizontal circular path about a vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of the angular velocity of ball (in radian/s) is
(a) 9
(b).18
(c) 27
(d) 36
A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is
A block of mass m is placed on a surface with a vertical cross-section given by y =x3/ 6. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is
(a) ⅓ m
(b) ½ m
(c) ⅙ m
(d) ⅔ m
A body of mass m=10−2 kg is moving in a medium and experiences a frictional force F=−kv2. Its initial speed is v0= 10 ms−1. If, after 10 s, its energy is ⅛ mv02, the value of k will be
(a) 10−3 kg m−1
(b) 10−3 kg s−1
(c) 10−4 kg m−1
(d) 10−1 kg m−1 s−1
The minimum force required to start pushing a body up a rough (frictional coefficient μ) inclined plane F1 while the minimum force needed to prevent it from sliding down is F2. If the inclined plane makes an angle θ from the horizontal such that tan θ= 2μ then the ratio F1/F2 is
(a) 4
(b) 1
(c) 2
(d) 3
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
(a) 2 sinΦ
(b) 2 cosΦ
(c) 2 tanΦ
(d) tanΦ
A block rests on a rough inclined plane making an angle of 300 with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is : (taken g =10 m/s2)
(a) 2.0
(b) 4.0
(c) 1.6
(d) 2.5
A horizontal force of 10 N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is 0.2. The weight of the block is-
(a) 20 N
(b) 50 N
(c) 100 N
(d) 2 N
Compare the functioning of alveoli in the lungs and nephrons in the kidneys with respect to their structure and functioning.
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