(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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$A$ cube of mass $m$ slides down an inclined right-angle trough. If the coefficient of kinetic friction between the cube and the trough is $\mu_k$,then the acceleration of the block is:

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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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Starting from rest,the time taken by a body sliding down on a rough inclined plane at $45^{\circ}$ with the horizontal is twice the time taken to travel on a smooth plane of the same inclination and same distance. Then the coefficient of kinetic friction is

DifficultTS EAMCET 2008

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

MediumAIEEE 2004

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The upper half of an inclined plane of inclination $\theta$ is perfectly smooth,while the lower half is rough. $A$ body starting from rest at the top comes back to rest at the bottom. The coefficient of friction $\mu$ for the lower half is given by:

DifficultAIEEE 2005

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$A$ cube of mass $m$ slides down an inclined right-angle trough. If the coefficient of kinetic friction between the cube and the trough is $\mu_k$,then the acceleration of the block is:

Starting from rest,the time taken by a body sliding down on a rough inclined plane at $45^{\circ}$ with the horizontal is twice the time taken to travel on a smooth plane of the same inclination and same distance. Then the coefficient of kinetic friction is

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