$A$ block of mass $m_1=1 \ kg$ and another mass $m_2=2 \ kg$ are placed together (see figure) on an inclined plane with an angle of inclination $\theta$. Various values of $\theta$ are given in List $I$. The coefficient of friction between the block $m_1$ and the plane is always zero. The coefficient of static and dynamic friction between the block $m_2$ and the plane are equal to $\mu=0.3$. In List $II$,expressions for the friction on block $m_2$ are given. Match the correct expression of the friction in List $II$ with the angles given in List $I$,and choose the correct option. The acceleration due to gravity is denoted by $g$. [Useful information: $\tan(5.5^{\circ}) \approx 0.1; \tan(11.5^{\circ}) \approx 0.2; \tan(16.5^{\circ}) \approx 0.3$]
List $I$ List $II$
$P. \theta=5^{\circ}$ $1. m_2 g \sin \theta$
$Q. \theta=10^{\circ}$ $2. (m_1+m_2) g \sin \theta$
$R. \theta=15^{\circ}$ $3. \mu m_2 g \cos \theta$
$S. \theta=20^{\circ}$ $4. \mu(m_1+m_2) g \cos \theta$

  • A
    $P-1, Q-1, R-1, S-3$
  • B
    $P-2, Q-2, R-2, S-3$
  • C
    $P-2, Q-2, R-2, S-4$
  • D
    $P-2, Q-2, R-3, S-3$

Explore More

Similar Questions

$A$ block is released from rest on a $45^\circ$ smooth incline and slides a distance '$d$'. The time taken to slide the same distance '$d$' on a rough incline is '$n$' times the time taken on the smooth incline. The coefficient of kinetic friction is

Difficult
View Solution

$A$ block of mass $5 \text{ kg}$ is placed on a rough inclined surface as shown in the figure. If $\vec{F}_1$ is the force required to just move the block up the inclined plane and $\vec{F}_2$ is the force required to just prevent the block from sliding down,then the value of $|\vec{F}_1|-|\vec{F}_2|$ is: [Use $g=10 \text{ m/s}^2$]

The upper half of an inclined plane of inclination $\theta$ is smooth,while the lower half is rough. If a block released from the top comes to rest at the bottom,what is the coefficient of friction between the block and the rough surface?

Difficult
View Solution

The force required to just move a body up the inclined plane is double the force required to just prevent the body from sliding down the plane. The coefficient of friction is $\mu$. The inclination $\theta$ of the plane is

Difficult
View Solution

To determine the coefficient of friction between a rough surface and a block,the surface is kept inclined at $45^{\circ}$ and the block is released from rest. The block takes a time $t$ in moving a distance $d$. The rough surface is then replaced by a smooth surface and the same experiment is repeated. The block now takes a time $t/2$ in moving down the same distance $d$. The coefficient of friction is

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo