(D) When a block is on the verge of sliding down an inclined plane,the angle of inclination $\theta$ is equal to the angle of repose.At this condition

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(D) When a block is on the verge of sliding down an inclined plane,the angle of inclination $\theta$ is equal to the angle of repose.At this condition,the coefficient of static friction $\mu$ is given by $\mu = \tan \theta$.Given $\sin \theta = \frac{3}{5}$.In a right-angled triangle,if the perpendicular is $3$ and the hypotenuse is $5$,then the base is $\sqrt{5^2 - 3^2} = \sqrt{25 - 9} = \sqrt{16} = 4$.Therefore,$\tan \theta = \frac{\text{perpendicular}}{\text{base}} = \frac{3}{4}$.Thus,$\mu = 0.75$.

Class 11 Physics Laws of Motion Motion (or rest) on Rough Inclined Surface

Medium

$A$ block of mass $4\, kg$ rests on an inclined plane. The inclination of the plane is gradually increased. It is found that when the inclination is $3$ in $5$ $\left( \sin \theta = \frac{3}{5} \right)$,the block just begins to slide down the plane. The coefficient of friction between the block and the plane is

A
$0.4$
B
$0.6$
C
$0.8$
D
$0.75$

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Class 11

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Laws of Motion

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Motion (or rest) on Rough Inclined Surface

What percentage of the total length of a chain can hang off the edge of a table without sliding,given that the coefficient of friction between the chain and the table is $0.25$?

Medium

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$A$ block of mass $15\, kg$ is resting on a rough inclined plane as shown in the figure. The block is tied by a horizontal string which has a tension of $50\, N$. The coefficient of friction between the surfaces of contact is $(g = 10\, m/s^2)$.

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The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction, when the angle of inclination of the plane is $60^{\circ}$ is

DifficultAP EAMCET 2019

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Consider a block kept on an inclined plane (inclined at $45^{\circ}$) as shown in the figure. If the force required to just push it up the incline is $2$ times the force required to just prevent it from sliding down,the coefficient of friction between the block and inclined plane $(\mu)$ is equal to

DifficultJEE MAIN 2023

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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 $10 \text{ N}$, the mass of the block is $\left(g=10 \text{ ms}^{-2}\right)$ (in $\text{ kg}$)

DifficultKCET 2018

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What percentage of the total length of a chain can hang off the edge of a table without sliding,given that the coefficient of friction between the chain and the table is $0.25$?

$A$ block of mass $15\, kg$ is resting on a rough inclined plane as shown in the figure. The block is tied by a horizontal string which has a tension of $50\, N$. The coefficient of friction between the surfaces of contact is $(g = 10\, m/s^2)$.

The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction, when the angle of inclination of the plane is $60^{\circ}$ is

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