Instantaneous Axis of Rotation

Q. A uniform rod of length $L$ (in between the supports) and mass m is placed on two hinges A and B. The rod breaks suddenly at length $\frac{L}{10}$ from the support B. Find the reaction at hinge A immediately after the rod breaks :

1. $\frac{9}{40}\text{mg}$
2. $\frac{19}{40}\text{mg}$
3. $\frac{\text{mg}}{2}$
4. $\frac{9}{20}\text{mg}$

Q.

What is cross-product used for?

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. The stick applies a force of $2\text{N}$ on the ring$(R=0.5\text{m})$ and the ring rolls without slipping on the ground as shown in figure. The coefficient of friction between the stick and the ring is

1. $0.4$
2. $0.3$
3. $0.2$
4. $0.5$

Q. A solid sphere of mass $0.50\text{kg}$ is kept at rest on horizontal surface. The coefficient of static friction between the solid sphere and the surface in contact is $\frac{2}{7}$. The maximum force that can be applied at the highest point of sphere in the horizontal direction so that the sphere dosen't slip on the surface is given by $\frac{x}{3}\text{N}$, then value of $x$ is
(Assume $g=10{\text{ms}}^{-2}$)

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. 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 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. The stick applies a force of $2\text{N}$ on the ring$(R=0.5\text{m})$ and the ring rolls without slipping on the ground as shown in figure. The coefficient of friction between the stick and the ring is

1. $0.4$
2. $0.3$
3. $0.2$
4. $0.5$

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