The upper half of an inclined plane of the inclination is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by,
C.
An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 m/s and the second part of mass 2 kg moves with second part of mass 2 kg moves with 8 m/s speed. If the third part flies off with 4 m/s speed, then its mass is,
3 kg
5 kg
7 kg
17 kg
B.
5 kg
We have,
p_{1} + p_{2} + p_{3} = 0 [ because p = mv]
Therefore,
1 x 12 i + 2 x 8 j + p_{3} = 0
Now. p_{3} = m_{3} v_{3}
This implies,
A person of mass 62 kg is inside of a lift of mass 940 kg and presses the button on control panel. The lift starts moving upwards with an acceleration 1.0 m/s^{2}. If g = 10 m/s^{2} ,the tension in the supporting cable is
9680 N
11000 N
1200 N
8600 N
B.
11000 N
A planet moving along an elliptical orbit is closer to the sun at a distance r_{1} and farthest away at a distance of r_{2}. if v_{1} and v_{2} are the linear velocities at these points respectively, then the ratio v_{1}/v_{2} is
r_{2}/r_{1}
(r_{2}/r_{1})^{2}
r_{1} /r_{2}
(r_{1}/r_{2})^{2}
A.
r_{2}/r_{1}
From the law of conservation of angular momentum
mr_{1}v_{1} = mr_{2}v_{2}
r_{1}v_{1} = r_{2}v_{2}
v_{1}/v_{2} = r_{2}/r_{1}