Deducing Mathematically

Q.

A shell acquires the initial velocity $v$ = 320 m/s, having made $n$ = 2.0 turns inside the barrel whose length is equal to $l$ = 2.0 m. Assuming that the shell moves inside the barrel with a uniform acceleration, find the angular velocity of its axial rotation at the moment when the shell escapes the barrel.

1. 

2. 

3. 

4. Data insufficient

Q.

A wheel rotates with a constant angular acceleration of 2.0 $\frac{rad}{s^2}$. If the wheel starts from rest, how many revolutions will it make in the first 10 seconds?

1. 32

2. 8

3. 16

4. 4

Q.

A fan is rotating with angular velocity 100 $\frac{rev}{sec}$. Then it is switched off. It takes 5 minutes to stop. (i) Find the total number of revolution made before it stops. (Assume uniform angular retardation) (ii)) Find the value of angular retardation (iii) Find the average angular velocity during this interval.

1. No. of revolutions = 15000

2. =

3. =

4. =

Q.

The wheel of a motor, accelerated uniformly from rest, rotates through 2.5 radian during the first second. Find the angle rotated during the next second.

1. 10 rad

2. 7.5 rad

3. 5 rad

4. 12.5 rad

Q.

Two particle A and B move on a circle. Initially Particle A and B are diagonally opposite to each other. Particle A moves with angular velocity $\pi \frac{rad}{sec}$, angular acceleration $\frac{\pi }{2}\frac{rad}{se{c}^2}$ and particle B moves with constant angular velocity $2\pi \frac{rad}{sec}$. Find the time after which both the particle A and B will collide.

1. 

2. 

3. 

4. 

Q. Figure below shows a small wheel fixed coaxially on a bigger one of double the radius. The system rotates about the common axis. The strings supporting A and B do not slip on the wheels. If 'x' and 'y' be the distances travelled by A and B in the same time interval, then

1. x = 2y
2. y = 2x
3. x = y
4. None of these

Q. A wheel initially at rest, is now rotated with a uniform angular acceleration. The wheel rotates through an angle ${\theta }_1$ in first one second and through an additional angle ${\theta }_2$ in the next one second. The ratio $\frac{{\theta }_2}{{\theta }_1}$ is

1. 4
2. 3
3. 1
4. 2

Q. A wheel is at rest. Its angular velocity increases uniformly and becomes 60 rad/sec after 5 sec. The total angular displacement is

1. 600 rad
2. 75 rad
3. 300 rad
4. 150 rad

Q. As a part of a maintenance inspection the compressor of a jet engine is made to spin according to the graph as shown. The number of revolutions made by the compressor during the test is

1. 9000
2. 11250
3. 16570
4. 12750

Q. A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches 100 rev/sec in 4 secs. Its angular acceleration is.

1. $25\frac{rev}{s^2}$
2. $500\frac{rev}{s^2}$
3. $100\frac{rev}{s^2}$
4. $625\frac{rev}{s^2}$