Rotational Power

Q. The angular velocity of a body is $\overrightarrow{\omega }=2\hat{i}+3\hat{j}+4\hat{k}$ and a torque $\overrightarrow{\tau }=\hat{i}+2\hat{j}+3\hat{k}$ acts on it. The rotational power will be

1. 20 W
2. 15 W
3. $\sqrt{17}W$
4. $\sqrt{14}W$

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. 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. When a solid sphere is released on a fixed rough inclined plane so that it rolls purely. When it reaches the ground it has the translational kinetic energy of $100J$. What would have been the translational kinetic energy at the bottom, if the plane was smooth? (In $J$) :-

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. 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. 1000 J/s
3. 1250 J/s
4. 5000 J/s

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

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

Q. A force $F=10\text{N}$ is acting on pulley of mass $M=2\text{kg}$ and radius $R=1\text{m}$ as shown in the figure. If pulley is rotating with constant angular velocity $\omega =4\text{rad/s}$. Find the power delivered by the force $F$ to the pulley.

1. $20\text{J/s}$
2. $10\text{J/s}$
3. $30\text{J/s}$
4. $40\text{J/s}$

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