(C) Using the third equation of motion,$v^{2} = u^{2} - 2as$. At the highest point,the final velocity $v = 0$.Therefore,$0 = u^{2} - 2as$,which gives

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(C) Using the third equation of motion,$v^{2} = u^{2} - 2as$. At the highest point,the final velocity $v = 0$.Therefore,$0 = u^{2} - 2as$,which gives $s = \frac{u^{2}}{2a}$.For an object on a smooth inclined plane,the acceleration $a = g \sin \theta$.Thus,the distance traveled is $s = \frac{u^{2}}{2g \sin \theta}$.Since $u$ and $g$ are constant,$s \propto \frac{1}{\sin \theta}$.Therefore,$\frac{x_{1}}{x_{2}} = \frac{\sin \theta_{2}}{\sin \theta_{1}} = \frac{\sin 30^{\circ}}{\sin 60^{\circ}}$.Substituting the values,$\frac{x_{1}}{x_{2}} = \frac{1/2}{\sqrt{3}/2} = \frac{1}{\sqrt{3}}$.Hence,the ratio $x_{1}: x_{2}$ is $1: \sqrt{3}$.

Class 11 Physics Newton's Laws of Motion and Friction Motion (or rest) on Rough Inclined Surface

Medium

When an object is shot from the bottom of a long smooth inclined plane kept at an angle $60^{\circ}$ with the horizontal,it can travel a distance $x_{1}$ along the plane. But when the inclination is decreased to $30^{\circ}$ and the same object is shot with the same velocity,it can travel $x_{2}$ distance. Then $x_{1}: x_{2}$ will be

NEET 2019 All NEET

A
$1: \sqrt{2}$
B
$\sqrt{2}: 1$
C
$1: \sqrt{3}$
D
$1: 2 \sqrt{3}$

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Class 11

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Newton's Laws of Motion and Friction

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Motion (or rest) on Rough Inclined Surface

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NEET 2019 Paper All NEET years →

Two touching blocks $1$ and $2$ are placed on an inclined plane forming an angle $60^{\circ}$ with the horizontal. The masses are $m_1$ and $m_2$ and the coefficients of friction between the inclined plane and the two blocks are $1.5 \mu$ and $1.0 \mu$, respectively. The force of reaction between the blocks during the motion is ($g=$ acceleration due to gravity).

DifficultTS EAMCET 2019

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The time taken by an object to slide down a $45^{\circ}$ rough inclined plane is $n$ times the time it takes to slide down a perfectly smooth $45^{\circ}$ inclined plane. The coefficient of kinetic friction between the object and the inclined plane is:

DifficultAIEEE 2005

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$A$ uniform rod of mass $20 \ kg$ and length $5 \ m$ leans against a smooth vertical wall making an angle of $60^{\circ}$ with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (take $g=10 \ m/s^2$)

DifficultNEET 2025

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$A$ block of mass $1 \ kg$ is pushed up a surface inclined to the horizontal at an angle of $60^{\circ}$ by a force of $10 \ N$ parallel to the inclined surface as shown in the figure. When the block is pushed up by $10 \ m$ along the inclined surface,the work done against the frictional force is: $\left[g=10 \ m/s^2, \mu_s = 0.1\right]$

DifficultJEE MAIN 2024

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Consider three masses $m_1, m_2$ and $m_3$ $(m_1 > m_2 > m_3)$ that are at rest on an inclined plane as shown in the figure. The angle of inclination $(\theta)$ of the plane is gradually increased until the masses just begin to slide. (Assume the coefficient of static friction between the masses and the surface is constant). Then,which of the following statements is correct?

MediumAP EAMCET 2022

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The time taken by an object to slide down a $45^{\circ}$ rough inclined plane is $n$ times the time it takes to slide down a perfectly smooth $45^{\circ}$ inclined plane. The coefficient of kinetic friction between the object and the inclined plane is:

$A$ uniform rod of mass $20 \ kg$ and length $5 \ m$ leans against a smooth vertical wall making an angle of $60^{\circ}$ with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (take $g=10 \ m/s^2$)

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