Direction of Friction

Q. A uniform sphere of mass ${}^{\prime }{m}^{\prime }$ is given some angular velocity about a horizontal axis through its centre and gently placed on a plank of mass ${}^{\prime }{m}^{\prime }$. The co-efficient of friction between the two is $\mu$. The plank rests on a smooth horizontal surface. The initial acceleration of the centre of the sphere relative to the plank will be:

1. zero
2. $\mu g$
3. $\left(\frac{7}{5}\right)\mu g$
4. $2\mu g$

Q.

Comprehension Type: A uniform thin cylindrical disk of mass M ad radius R is attached to two identical mass less springs of springs constant k which are fixed to the wall as show in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its center. The axle is mass less and both the springs and the axle are in horizontal plane. The un-stretched length of each springs is L. The disk is initially at its equilibrium position with its center of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity $\overrightarrow{(}V{)}_0=V_0\hat{i}$ The coefficient of friction is $\mu$.

The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is

1. - kx

2. - 2kx

3. $-\frac{2kx}{3}$

4. $-\frac{4kx}{3}$

Q. A uniform sphere of mass ${}^{\prime }{m}^{\prime }$ is given some angular velocity about a horizontal axis through its centre and gently placed on a plank of mass ${}^{\prime }{m}^{\prime }$. The co-efficient of friction between the two is $\mu$. The plank rests on a smooth horizontal surface. The initial acceleration of the centre of the sphere relative to the plank will be:

1. zero
2. $\mu g$
3. $\left(\frac{7}{5}\right)\mu g$
4. $2\mu g$

Q. A force of 15 N rotates a sphere, resting on a horizontal surface with friction, in the clockwise direction. The direction of frictional force .

1. is forwards
2. is backwards
3. can't be determined

Q. To sharpen the blade of a knife by rubbing it against a surface, which of the following will be most suitable?

एक चाकू की ब्लैड को पृष्ठ पर रगड़कर इसे धारदार बनाने के लिए, निम्नलिखित में से कौनसा सबसे उपयुक्त होगा?

1. Plastic block
   
   प्लास्टिक का गुटका
   
2. Wooden block
   
   लकड़ी का गुटका
   
3. Glass block
   
   काँच का गुटका
   
4. Stone
   
   पत्थर
   

Q. A disk and a solid sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

1. Both reach at the same
2. Disk
3. Sphere
4. Depends on their masses

Q. A ball moving on a frictionless surface may have rotatory kinetic energy.

1. True
2. False

Q.

A rigid body of mass 'M' and radius R is rolling without sliding, along with bock of radius of gyration K, and mass $m_1$, then find the minimum value of friction coefficient $\mu$?

1. $\frac{M{k}^2}{R^2\{M+m(1+\frac{k^2}{R^2}\left)\right\}}$

2. $\frac{M{k}^2}{R^2\{M+m(1+\frac{k^2}{R^2}\left)\right\}}$

3. $\frac{M{R}^2}{k^2\{M+m(1+\frac{k^2}{R^2}\left)\right\}}$

4. $\frac{M{R}^2}{k^2\{M+m(1+\frac{k^2}{R^2}\left)\right\}}$

Q. A uniform sphere of mass ${}^{\prime }{m}^{\prime }$ is given some angular velocity about a horizontal axis through its centre and gently placed on a plank of mass ${}^{\prime }{m}^{\prime }$. The co-efficient of friction between the two is $\mu$. The plank rests on a smooth horizontal surface. The initial acceleration of the centre of the sphere relative to the plank will be:

1. zero
2. $\mu g$
3. $\left(\frac{7}{5}\right)\mu g$
4. $2\mu g$

Q. Two forces of magnitude $F$ each are acting on a uniform disc kept on a horizontal surface as shown in the figure. The disc performs rolling without slipping. If the frictional force by the horizontal surface is $nF$. The value of $n$ is

Q. A thin ring of mass $2\text{kg}$ and radius $1\text{m}$ is rolling without slipping on a horizontal plane with velocity $1\text{m/s}$. A small ball of mass $1\text{kg}$ and moving with velocity $2\text{m/s}$ in the opposite direction, hits the ring at a height of $1.8\text{m}$ and goes vertically up with velocity of $1\text{m/s}$. Immediately after the collision, which of the following is true?

1. Ring undergoes pure rotation about its axis through the centre of mass.
2. Ring comes to a complete stop.
3. Friction on the ring by the ground is to the left.
4. There is no friction between the ring and ground.

Q. For a ball rolling down an incline with $v_{\mathrm{cm}}=\mathrm{\omega r}$ , static friction acts in the direction of $v_{\mathrm{cm}}$.

1. False
2. True

Q. The frictional force on the ring (as shown in figure) is

1. $\frac{F}{3}$ towards left
2. $\frac{2F}{3}$ towards left
3. $\frac{F}{3}$ towards right
4. Zero

Q. Newton's laws can be applied to all the particles of an object in an inertial frame.

1. False
2. True