Static, kinetic and rolling friction — practice questions

Question 1 · difficulty L2 · understanding

An inclined plane is bent in such a way that the vertical cross-section is given by $$y = {{{x^2}} \over 4}$$ where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction $$\mu$$ = 0.5, the maximum height in cm at which a stationary block will not slip downward is _________ cm.

Question 2 · difficulty L2 · understanding

The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be _________ N. [g = 10 ms $$-$$2 ]

Question 3 · difficulty L2 · understanding

A block is sliding down on an inclined plane of slope $\theta$ and at an instant $t=0$ this block is given an upward momentum so that it starts moving up on the inclined surface with velocity $u$. The distance $(S)$ travelled by the block before its velocity become zero, is $\_\_\_\_$ . (g = gravitational acceleration)

• A. $\frac{2 u^2}{\mathrm{~g} \cos \theta}$
• B. $\frac{u^2}{\sqrt{2} g \cos \theta}$
• C. $\frac{u^2}{2 g \sin \theta}$
• D. $\frac{u^2}{2 g \cos \theta}$

Question 4 · difficulty L2 · understanding

A cubic block of mass $m$ is sliding down on an inclined plane at $60^{\circ}$ with an acceleration of $\frac{g}{2}$, the value of coefficient of kinetic friction is

• A. $\frac{\sqrt{3}}{2}$
• B. $\frac{\sqrt{2}}{3}$
• C. $1-\frac{\sqrt{3}}{2}$
• D. $\sqrt{3}-1$

Question 5 · difficulty L2 · understanding

A heavy box of mass $$50 \mathrm{~kg}$$ is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :

• A. 1470 N
• B. 147 N
• C. 1.47 N
• D. 14.7 N

Question 6 · difficulty L2 · understanding

A $$2 \mathrm{~kg}$$ brick begins to slide over a surface which is inclined at an angle of $$45^{\circ}$$ with respect to horizontal axis. The co-efficient of static friction between their surfaces is:

• A. 1
• B. 1.7
• C. 0.5
• D. $$\frac{1}{\sqrt{3}}$$

Question 7 · difficulty L2 · understanding

Given below are two statements : Statement (I) : The limiting force of static friction depends on the area of contact and independent of materials. Statement (II) : The limiting force of kinetic friction is independent of the area of contact and depends on materials. In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Statement I is incorrect but Statement II is correct
• B. Both Statement I and Statement II are correct
• C. Both Statement I and Statement II are incorrect
• D. Statement I is correct but Statement II is incorrect

Question 8 · difficulty L2 · understanding

As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle $$30^\circ$$, with horizontal. For $$\mu_s=0.25$$, the block will just start to move for the value of F : [Given $$g=10~\mathrm{ms}^{-2}$$]

• A. 25.2 N
• B. 35.7 N
• C. 20 N
• D. 33.3 N

Question 9 · difficulty L2 · understanding

A block of mass $$5 \mathrm{~kg}$$ is placed at rest on a table of rough surface. Now, if a force of $$30 \mathrm{~N}$$ is applied in the direction parallel to surface of the table, the block slides through a distance of $$50 \mathrm{~m}$$ in an interval of time $$10 \mathrm{~s}$$. Coefficient of kinetic friction is (given, $$g=10 \mathrm{~ms}^{-2}$$):

• A. 0.25
• B. 0.75
• C. 0.60
• D. 0.50

Question 10 · difficulty L2 · understanding

A body of mass $10 \mathrm{~kg}$ is moving with an initial speed of $20 \mathrm{~m} / \mathrm{s}$. The body stops after $5 \mathrm{~s}$ due to friction between body and the floor. The value of the coefficient of friction is: (Take acceleration due to gravity $g=10 \mathrm{~ms}^{-2}$ )

• A. 0.3
• B. 0.2
• C. 0.5
• D. 0.4