Deducing Mathematically

Q.

A wheel rotates with a constant 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. 8

2. 32

3. 16

4. 4

Q. Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time.

Q. A wheel rotates with a constant angular acceleration of $3.6{\text{rad/s}}^2$. If angular velocity of the wheel is $4.0\text{rad/s}$ at time $t_0=0$, what angle does the wheel rotate in $1\text{s}$? What will be its angular velocity at $t=1\text{s}$?

1. $\theta =2.2\text{rad},\omega =7.6\text{rad/s}$
2. $\theta =2.2\text{rad},\omega =0.4\text{rad/s}$
3. $\theta =5.8\text{rad},\omega =7.6\text{rad/s}$
4. $\theta =5.8\text{rad},\omega =0.4\text{rad/s}$

Q.

Two discs of moment of inertia $I_1$ , $I_2$ are rotating with angular velocities ${\omega }_1$, ${\omega }_2$ along collinear axes passing through their centre of mass and perpendicular to their plane. If the two are made to rotate combined along the same axis the rotational KE of system will be

1. 

2. 

3. 

4. 

Q. A body is projected with an initial velocity of $20\hat{i}+20\hat{j}$. It clears a wall at a distance of 20 m. Find the velocity when it clears the wall.

1. 
2. 
3. 
4. 

Q. A wheel rotates with a constant angular acceleration of $3.6{\text{rad/s}}^2$. If angular velocity of the wheel is $4.0\text{rad/s}$ at time $t_0=0$, what angle does the wheel rotate in $1\text{s}$? What will be its angular velocity at $t=1\text{s}$?

1. $\theta =5.8\text{rad},\omega =0.4\text{rad/s}$
2. $\theta =2.2\text{rad},\omega =0.4\text{rad/s}$
3. $\theta =5.8\text{rad},\omega =7.6\text{rad/s}$
4. $\theta =2.2\text{rad},\omega =7.6\text{rad/s}$

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.

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. $t=2sec$

2. $t=1sec$

3. $t=4sec$

4. $t=\frac{4\pm \sqrt{14}}{2}sec$

Q. Two rigid bodies A and B rotate with rotational kinetic energies $E_A$ and $E_B$ respectively. The moments of inertia of A and B about the axis of rotation are $I_A$ and $I_B$ respectively. If $I_A=I_B/4$ and $E_A/100=E_B$ the ratio of angular momentum $\left(L_A\right)$ of A to the angular momentum $\left(L_B\right)$ of B is

1. 25
2. 5
3. 5/4
4. 1/4

Q. The angular position of a point on the rim of a rotating wheel is given by $\theta =4t-3t^2+t^3$, where $\theta$ is in radians and $t$ is in seconds. What is the instantaneous angular acceleration at $t=2\text{sec}$?

1. $4{\text{rad/s}}^2$
2. $2{\text{rad/s}}^2$
3. $6{\text{rad/s}}^2$
4. $3{\text{rad/s}}^2$

Q. A wheel rotates with a constant angular acceleration of $3.6{\text{rad/s}}^2$. If angular velocity of the wheel is $4.0\text{rad/s}$ at time $t_0=0$, what angle does the wheel rotate in $1\text{s}$? What will be its angular velocity at $t=1\text{s}$?

1. $\theta =5.8\text{rad},\omega =0.4\text{rad/s}$
2. $\theta =2.2\text{rad},\omega =0.4\text{rad/s}$
3. $\theta =5.8\text{rad},\omega =7.6\text{rad/s}$
4. $\theta =2.2\text{rad},\omega =7.6\text{rad/s}$

Q. (a) What is the largest average velocity of blood flow in an artery of radius $2\times {10}^{-3}m$ if the flow must remain lanimar? (b) What is the corresponding flow rate ? (Take viscosity of blood to be $2.084\times {10}^{-3}Pas$).

Q. The angular velocity of second's hand of a watch will be :-

1. $30\pi \text{rad/sec}$
2. $\frac{\pi }{30}\text{rad/sec}$
3. $60\pi \text{rad/ sec}$
4. $\frac{\pi }{60}\text{rad/sec}$

Q. The angular position of a rotating disc is given as $\theta =6t^2+5t-4$ where $\theta$ is in radians, $t$ is in seconds. What is the average angular velocity for the first time interval from $t=0\text{(s)}$ to $t=4\text{(s)}$?

1. $29\text{rad/s}$
2. $18\text{rad/s}$
3. $4\text{rad/s}$
4. $27\text{rad/s}$

Q. A disc rotates about its axis with a constant angular acceleration of$4\frac{rad}{s^2}.$Radial acceleration of a particle at a distance of$1cm$from the axis at the end of$1sec$is.

1. $16\frac{cm}{s^2}$
2. $1.6\frac{cm}{s^2}$
3. $16\frac{m}{s^2}$
4. $1.6\frac{m}{s^2}$

Q. A fan is running at $300\text{rpm}$. It is switched off. It comes to rest by uniformly decreasing its angular speed in $10$ seconds. The total number of revolutions in this period are :-

1. $15$
2. $25$
3. $35$
4. $30$