Direction of Friction

Q. A cylinder is pulled on a horizontal floor without slipping by a string wrapped around it. If the string is pulled horizontally from the top with a velocity v/2, then centre of the cylinder moves with a velocity v(c) equal to- 1)v/4, 2)2v, 3)v/2, 4)zer

Q. A block rests on a rough inclined plane making an angle of ${30}^{\circ }$ with horizontal. The coefficient of static friction between the block and inclined plane is 0.8. If the frictional force on the block is 10N, the mass of the block in kg is (g=10$m/s^2$)

1. 5 kg
2. 20 kg
3. 2 kg
4. 0.5 kg

Q. A ball rolls down an inclined plane and acquires a velocity $v_r,$ when it reaches the bottom of the plane. If the same ball slides from the same height on smooth inclined plane and acquires a velocity $v_B$ at bottom. Which of the following statements is/are incorrect?

1. $v_r<v_s$, because some work is done by the rolling ball against the frictional force.
2. $v_r>v_s$. because the angular velocity acquired makes the rolling ball to travel faster
3. $v_r=v_s$, because kinetic energy of two balls is same at bottom of planes
4. $v_r<v_s$, because the rolling ball acquires rotational as well as translational kinetic energy

Q. Or 2 gram block attached to an ideal spring with spring constant of 18 Newton per metre oscillates on a horizontal frictionless surface in the spring is 4.0cm shorter than the its equilibrium Length speed of block is 17 metre per second a greater speed of block is 1.)4m/s 2

Q. Why is horizontal component of velocity always constant in a projectile motion?

Q. what is the speed at the highest point of path of projectile?

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 in a non-inertial frame

1. True
2. False

Q. Why is horizontal component of velocity always constant in a projectile motion?

Q. A solid sphere of Mass $M$ and radius $R$ is pulled horizontally on a rough surface as shown in the figure. Choose the incorrect alternative(s).

1. The magnitude of the frictional force is $F/3$.
2. The frictional force on the sphere acts forward.
3. The acceleration of the centre of mass is $2F/3M$.
4. The acceleration of the centre of mass is $5F/7M$.

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 small disc and a large disc are connected by a belt. The small disc whose radius is 15 cm rotates at an angular speed of 360 rpm. The radius of large disc having mass 8 kg is 45 cm. The kinetic energy of large disc is nearly equal to ( Assume ${\pi }^2=10$)

1. 60 J
2. 64 J
3. 120 J
4. 45 J

Q. how to solve n^{th} second problems in horizontal motion when a body stops under cons†an t deceleration and then reverses its direction.

Q. A disk and a 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. Depends on their masses
2. Disk
3. Sphere
4. Both reach at the same time.

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.

In the arrangement shown in the figure, there is friction between the blocks of masses m and 2m which are in contact. The ground is smooth. The mass of the suspended block is m. The block of mass m which is kept on mass 2m is stationary with respect to a block of mass 2m. The force of friction between m and 2m is (pulleys and string are lig frictionless):

1. $\frac{mg}{3}$
2. $\frac{mg}{\sqrt{2}}$
3. $\frac{mg}{2}$
4. $\frac{mg}{4}$

Q. In the question, in which direction the net torque on the pulley will act? ($M_1$ > $M_2$)

1. Clockwise
2. Anticlockwise

Q. The distance moved by wedge when $2kg$ block completely slides down the wedgekept on a smooth horizontal surface

1. $3.8\text{m}$
2. $1.9\text{m}$
3. $2\text{m}$
4. $1.6\text{m}$