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Standard XII

Physics

Kinetic Friction

A ring takes ...

Question

A ring takes time $t_{1}$ and $t_{2}$ for sliding down and rolling down an inclined plane of length $L$ respectively for reaching the bottom. The ratio of $t_{1}$ and $t_{2}$ is

\sqrt{2} : 1

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1 : \sqrt{2}

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1 : 2

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2 : 1

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Solution

The correct option is B $1 : \sqrt{2}$
$\begin{matrix} f o r s l i d i n g a = g sin θ t_{1} = \sqrt{\frac{2 l}{g sin θ}} f o r r o l l i n g a = \frac{g sin θ}{2} t_{2} = \sqrt{2} . \sqrt{\frac{2 l}{g sin θ}} = \sqrt{2} t_{1} \Rightarrow \frac{t_{1}}{t_{2}} = \frac{1}{\sqrt{2}} \end{matrix}$
$∴$ Option $B$ is correct .

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Similar questions

Q. A ring takes time

t_{1}

in slipping down an inclined plane of length L, whereas it takes time

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Q. An object is placed on the surface of a smooth inclined plane of inclination

θ

it takes time

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to reach the bottom if the some object is allowed to slide down a rough inclined plane of inclination

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it takes time

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Q. The ratio of time taken by a body to slide down along a rough inclined plane to an identical smooth inclined plane for angle of inclination and coefficient of friction are as follows:-

S. no.	Ratio of times	Angle of inclinations	Coefficient of frictions
1.	$t_{1} / t_{2} = 2$	$θ = 30^{0}$	$μ_{1}$
2.	$t_{1} / t_{2} = 4$	$θ = 45^{0}$	$μ_{2}$
3.	$t_{1} / t_{2} = 3$	$θ = 30^{0}$	$μ_{3}$

Then the correct relation between

μ_{1}, μ_{2}, μ_{3}

is:

A block, released from rest from the top of a smooth inclined plane of angle of inclination $θ_{1}$ , reaches the bottom in time $t_{1}$ . The same block, released from rest from the top of another smooth inclined plane of angle of inclination $θ_{2}$ , reaches the bottom in time $t_{2}$ . If the two inclined planes have the same height, the relation between $t_{1}$ and $t_{2}$ is

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A ring takes time t1 and t2 for sliding down and rolling down an inclined plane of length L respectively for reaching the bottom. The ratio of t1 and t2 is

The correct option is B 1:√2forslidinga=gsinθt1=√2lgsinθforrollinga=gsinθ2t2=√2.√2lgsinθ=√2t1⇒t1t2=1√2∴ Option B is correct .

A ring takes time $t_{1}$ and $t_{2}$ for sliding down and rolling down an inclined plane of length $L$ respectively for reaching the bottom. The ratio of $t_{1}$ and $t_{2}$ is