SATHEE: Laws Of Motion Question 386

Laws Of Motion Question 386

Question: The time taken by a body in sliding down a rough inclined plane of angle of inclination $45^{\circ}$ is n times the time taken by the same body in slipping down a similar frictionless plane. The coefficient of dynamic friction between the body and the plane will be

Options:

A) $1 / (1 - n^{2})$

B) $1 - (1 / n^{2})$

C) Ö $1 - (1 / n^{2})$

D) Ö $1 / (1 - n^{2})$

Show Answer

Answer:

Correct Answer: B

Solution:

Acceleration when there is no friction is $a = g \sin θ$ and acceleration when friction is there is

$a^{'} = (g \sin θ - μ g \cos θ)$

We know that $s = u t + \frac{1}{2} a t^{2},$ under condition of $u = 0,$

gives, $t = \sqrt{(2 s / a)}$ .

Therefore $t^{'} t = \sqrt{(a / a^{'})}$ .

For our case we get

$n = \sqrt{[g \sin θ / (g \sin θ - μ g \cos θ)]}$

$\Rightarrow n^{2} = g \sin θ / (g \sin θ - μ g \cos θ) = 1 / (1 - μ \cot θ)$ but $θ = 45^{o}$

$\Rightarrow \cot θ = 1 ∴ n^{2} = 1 / (1 - μ)$ or $μ = 1 - (1 / n^{2})$

Laws Of Motion Question 386

Question: The time taken by a body in sliding down a rough inclined plane of angle of inclination $45^{\circ}$ is n times the time taken by the same body in slipping down a similar frictionless plane. The coefficient of dynamic friction between the body and the plane will be

Options:

Answer:

Solution:

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Laws Of Motion Question 386

Question: The time taken by a body in sliding down a rough inclined plane of angle of inclination 45∘ is n times the time taken by the same body in slipping down a similar frictionless plane. The coefficient of dynamic friction between the body and the plane will be

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: The time taken by a body in sliding down a rough inclined plane of angle of inclination $45^{\circ}$ is n times the time taken by the same body in slipping down a similar frictionless plane. The coefficient of dynamic friction between the body and the plane will be