Instantaneous Axis of Rotation

Q. A solid sphere is rolling purely on a horizontal surface. The angular velocity of sphere about its central axis is 2 $\frac{rad}{s}$ and it has m = 4 kg and R = 2m. What is the total kinetic energy of the sphere?

1. $\frac{148}{5}J$
2. $\frac{124}{5}J$
3. 100 J
4. 25 J

Q. A solid sphere of mass 5 kg and radius 10 m is rolling purely on a horizontal surface as shown in the figure. The separation of P from A (point of contact) is 7 m. If the sphere has an angular velocity about an axis through its centre of mass as 2 $\frac{rad}{sec},$ what is the speed of the point P at this instant ?

1. 20 m/s
2. 32 m/s
3. 14 m/s
4. 18 m/s

Q. A sphere is rolling purely on a horizontal surface. What is the velocity of its instantaneous axis of rotation with respect to the ground if its centre of mass moves with a velocity of 10 m/s in the forward direction ?(Radius = 10 m)

1. 1 m/s
2. 100 m/s
3. 5 m/s
4. 0 m/s

Q. A ball rolls down an incline. The instantaneous axis of rotaion of any point on the ball passes through the point in contact with the incline.

1. True
2. False

Q. End $A$ of a rod $AB$ is being pulled on the floor with a constant velocity $v_0$ as shown. Taking the length of the rod as $l$, at an instant when the rod makes an angle ${37}^{\circ }$ with the horizontal, calculate


The velocity of end $B$

1. $\frac{3}{5}{v}_0$
2. $\frac{4}{3}{v}_0$
3. $\frac{5}{3}{v}_0$
4. $\frac{5}{4}{v}_0$

Q. End $A$ of a rod $AB$ is being pulled on the floor with a constant velocity $v_0$ as shown. Taking the length of the rod as $l$, at an instant when the rod makes an angle ${37}^{\circ }$ with the horizontal, calculate

The angular velocity of the rod

1. $\frac{5v_0}{3l}$
2. $\frac{3v_0}{5l}$
3. $\frac{5v_0}{4l}$
4. $\frac{4v_0}{5l}$

Q. End $A$ of a rod $AB$ is being pulled on the floor with a constant velocity $v_0$ as shown. Taking the length of the rod as $l$, at an instant when the rod makes an angle ${37}^{\circ }$ with the horizontal, calculate



The velocity of the CM of the rod

1. $\frac{5}{7}{v}_0$ at $ta{n}^{-1}\frac{4}{3}$ below horizontal
2. $\frac{5}{7}{v}_0$ at $ta{n}^{-1}\frac{3}{4}$ below horizontal
3. $\frac{5}{6}{v}_0$ at $ta{n}^{-1}\frac{3}{4}$ below horizontal
4. $\frac{4}{5}{v}_0$ at $ta{n}^{-1}\frac{3}{4}$ below horizontal

Q. A disc of radius $0.2\text{m}$ is rolling with slipping on a flat horizontal surface as shown in the figure. The instantaneous centre of rotation is (the lowest contact point is O and centre of disc is C)

1. zero
2. $0.1\text{m}$ above O on line OC
3. $0.2\text{m}$ below O on line OC
4. $0.2\text{m}$ above O on line OC

Q. Two blocks are moving as shown. The ratio of$\frac{v_1}{v_2}$ is

1. $\frac{\sin {\theta }_1}{\sin {\theta }_2}$
2. $\frac{\sin {\theta }_2}{\sin {\theta }_1}$
3. $\frac{\cos {\theta }_2}{\cos {\theta }_1}$
4. $\frac{\cos {\theta }_1}{\cos {\theta }_2}$

Q. A uniform plank leans against a cylindrical body as shown in figure. The right end of plank slides at a constant speed of v = 2m/s. If R = 1m, then angular velocity of the plank when $\theta ={37}^{\circ }$ is (Write upto two digits after the decimal point.)