Rotational Power

Q. Calculate the torque developed by an airplane engine whose output is $3200\text{HP}$ at an angular velocity of $2400\text{rev/min}$. $(1\text{HP}=746\text{J/s})$

1. $9498\text{N-m}$
2. $1273\text{N-m}$
3. $2984\text{N-m}$
4. $5000\text{N-m}$

Q. Due to application of a torque having a magnitude of 20 N-m, a ring is rotating at an angular velocity of 250 $\frac{rad}{s}$ at any given instant. What is the power delivered at this moment?

1. 2500 J/s
2. 5000 J/s
3. 1000 J/s
4. 1250 J/s

Q. A uniform solid cylinder of radius $R=15\text{cm}$ rolls over a horizontal plane passing into an inclined plane forming an angle $\alpha ={30}^{\circ }$ with the horizontal. Find the maximum value of the velocity $v_{\circ }$ which still permits the cylinder to roll onto the inclined plane section without a jump. Assume there is no sliding between the cylinder and surfaces.

1. $1\text{m/s}$
2. $2\text{m/s}$
3. $4\text{m/s}$
4. 
   $0.5\text{m/s}$

Q. An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min. What torque does it deliver

1. 350 N-m
2. 440 N-m
3. 531 N-m
4. 628 N-m

Q. Engine of a car supplies constant power to the wheels of car, then

1. displacement of the car is proportional to $t^2$.
2. acceleration of the car is proportional to $t^{-1}$.
3. velocity of the car is proportional to $t^{1/2}$.
4. displacement of the car is proportional to $t^3$.