A block of mass slides down the plane inclined at an angle with an acceleration . The value of coefficient of kinetic friction will be [2023]

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Q.
A block of mass $m$ slides down the plane inclined at an angle $30 °$ with an acceleration $\frac{g}{4}$ . The value of coefficient of kinetic friction will be [2023]

1 $\frac{2 \sqrt{3} + 1}{2}$

2 $\frac{1}{2 \sqrt{3}}$

3 $\frac{\sqrt{3}}{2}$

4 $\frac{2 \sqrt{3} - 1}{2}$

Ans.
(2)

$M g \sin 30 ° - μ m g \cos 30 ° = m a$

$\frac{g}{2} - \frac{\sqrt{3}}{2} μ g = \frac{g}{4}$

$\frac{\sqrt{3}}{2} μ = \frac{1}{4}$

$\Rightarrow μ = \frac{1}{2 \sqrt{3}}$

Solution

Q.
A block of mass $m$ slides down the plane inclined at an angle $30 °$ with an acceleration $\frac{g}{4}$ . The value of coefficient of kinetic friction will be [2023]

1 $\frac{2 \sqrt{3} + 1}{2}$

2 $\frac{1}{2 \sqrt{3}}$

3 $\frac{\sqrt{3}}{2}$

4 $\frac{2 \sqrt{3} - 1}{2}$

Ans.
(2)

$M g \sin 30 ° - μ m g \cos 30 ° = m a$

$\frac{g}{2} - \frac{\sqrt{3}}{2} μ g = \frac{g}{4}$

$\frac{\sqrt{3}}{2} μ = \frac{1}{4}$

$\Rightarrow μ = \frac{1}{2 \sqrt{3}}$

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Solution

Q. A block of mass m slides down the plane inclined at an angle 30° with an acceleration g4. The value of coefficient of kinetic friction will be [2023]

1 23+12

2 123

3 32

4 23-12

Ans. (2) Mgsin30°-μmgcos30°=ma g2-32μg=g4 32μ=14 ⇒ μ=123

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Q.
A block of mass $m$ slides down the plane inclined at an angle $30 °$ with an acceleration $\frac{g}{4}$ . The value of coefficient of kinetic friction will be [2023]

1 $\frac{2 \sqrt{3} + 1}{2}$

2 $\frac{1}{2 \sqrt{3}}$

3 $\frac{\sqrt{3}}{2}$

4 $\frac{2 \sqrt{3} - 1}{2}$

Ans.
(2)

$M g \sin 30 ° - μ m g \cos 30 ° = m a$

$\frac{g}{2} - \frac{\sqrt{3}}{2} μ g = \frac{g}{4}$

$\frac{\sqrt{3}}{2} μ = \frac{1}{4}$

$\Rightarrow μ = \frac{1}{2 \sqrt{3}}$