If →F→F is the force acting on a particle having position vector →r→r and →τ→τ be the torque of this force about the origin, then:
1. | →r⋅→τ≠0 and →F⋅→τ=0→r⋅→τ≠0 and →F⋅→τ=0 |
2. | →r⋅→τ>0 and →F⋅→τ<0→r⋅→τ>0 and →F⋅→τ<0 |
3. | →r⋅→τ=0 and →F⋅→τ=0→r⋅→τ=0 and →F⋅→τ=0 |
4. | →r⋅→τ=0 and →F⋅→τ≠0→r⋅→τ=0 and →F⋅→τ≠0 |
1. | b2b2 | 2. | b4b4 |
3. | b8b8 | 4. | b3b3 |
A uniform rod of length 200 cm200 cm and mass 500 g500 g is balanced on a wedge placed at 40 cm40 cm mark. A mass of 2 kg2 kg is suspended from the rod at 20 cm20 cm and another unknown mass mm is suspended from the rod at 160 cm160 cm mark as shown in the figure. What would be the value of mm such that the rod is in equilibrium?
(Take g=10 (m/s2)g=10 (m/s2)
1. | 16 kg16 kg | 2. | 112 kg112 kg |
3. | 12 kg12 kg | 4. | 13 kg13 kg |
1. | wxdwxd | 2. | wdxwdx |
3. | w(d−x)xw(d−x)x | 4. | w(d−x)dw(d−x)d |
A non-uniform bar of weight WW is suspended at rest by two strings of negligible weight as shown in the figure. The angles made by the strings with the vertical are 36.9∘36.9∘ and 53.1∘53.1∘ respectively. The bar is 22 m long. The distance dd of the center of gravity of the bar from its left end is:
(Take sin36.9∘=0.636.9∘=0.6 and sin53.1∘=0.853.1∘=0.8)
1. 6969 cm
2. 7272 cm
3. 7979 cm
4. 6565 cm
To maintain a rotor at a uniform angular speed of 200 rad/s,200 rad/s, an engine needs to transmit a torque of 180 N-m.180 N-m. What is the power required by the engine?
1. 33 kW33 kW
2. 36 kW36 kW
3. 28 kW28 kW
4. 76 kW76 kW