(A) To complete a vertical circular path,the minimum velocity $v$ at the bottom of the circle must be $v = \sqrt{5gR}$.Given $R = 2\ m$ and $g = 10\ m

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(A) To complete a vertical circular path,the minimum velocity $v$ at the bottom of the circle must be $v = \sqrt{5gR}$.Given $R = 2\ m$ and $g = 10\ m/s^2$,the required velocity is $v = \sqrt{5 \times 10 \times 2} = \sqrt{100} = 10\ m/s$.On the rough surface,the initial velocity $u = 20\ m/s$,final velocity $v = 10\ m/s$,and acceleration $a = -\mu g = -0.5 \times 10 = -5\ m/s^2$.Using the equation of motion $v^2 - u^2 = 2ax$:$10^2 - 20^2 = 2 \times (-5) \times x$$100 - 400 = -10x$$-300 = -10x$$x = 30\ m$.

Class 11 Physics Work, Energy, Power and Collision Vertical Circular Motion

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$A$ block of mass $m$ is given a velocity $20\ m/s$ on a horizontal rough surface of length $x\ m$. After the rough surface,there is a vertical circular path of radius $R = 2\ m$ which is frictionless. The block enters the circular path with the minimum velocity required to complete the path. Find the length of the rough surface $x$ if the coefficient of friction is $\mu = 0.5$.

A
$30$
B
$20$
C
$10$
D
$16$

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Work, Energy, Power and Collision

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Vertical Circular Motion

$A$ mass is performing vertical circular motion (see figure). If the average velocity of the particle is increased,then at which point will the string break?

MediumAIPMT 2000

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$A$ $2 \, kg$ stone at the end of a string $1 \, m$ long is whirled in a vertical circle at a constant speed. The speed of the stone is $4 \, m/s$. The tension in the string will be $52 \, N$ when the stone is:

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$A$ mass $m$ is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when

MediumNEET 2019

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In vertical circular motion of a bob,match the entries of List-$I$ with entries of List-$II$. Here,$v_0$ is the velocity of the bob at the lowest point.

List-$I$ (Speed at lowest point) List-$II$ (Possible situation)

$(P) v_0 = \sqrt{5 g \ell}$ $(1)$ Tension at lowest point $= 6 mg$

$(Q) v_0 = \sqrt{g \ell}$ $(2)$ String will slack for a finite time

$(R) v_0 = 2 \sqrt{g \ell}$ $(3)$ Bob will oscillate

$(S) v_0 = 3 \sqrt{g \ell}$ $(4)$ Tension at highest point $= 4 mg$

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$A$ particle is whirled in a vertical circle of radius $1.0 \ m$ using a string with one end fixed. If the ratio of maximum and minimum tension in the string is $\frac{5}{3}$,the minimum velocity of the particle during circular motion is ......... $ms^{-1}$.

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List-$I$ (Speed at lowest point)	List-$II$ (Possible situation)
$(P) v_0 = \sqrt{5 g \ell}$	$(1)$ Tension at lowest point $= 6 mg$
$(Q) v_0 = \sqrt{g \ell}$	$(2)$ String will slack for a finite time
$(R) v_0 = 2 \sqrt{g \ell}$	$(3)$ Bob will oscillate
$(S) v_0 = 3 \sqrt{g \ell}$	$(4)$ Tension at highest point $= 4 mg$

Similar Questions

$A$ mass is performing vertical circular motion (see figure). If the average velocity of the particle is increased,then at which point will the string break?

$A$ $2 \, kg$ stone at the end of a string $1 \, m$ long is whirled in a vertical circle at a constant speed. The speed of the stone is $4 \, m/s$. The tension in the string will be $52 \, N$ when the stone is:

$A$ mass $m$ is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when

$A$ particle is whirled in a vertical circle of radius $1.0 \ m$ using a string with one end fixed. If the ratio of maximum and minimum tension in the string is $\frac{5}{3}$,the minimum velocity of the particle during circular motion is ......... $ms^{-1}$.

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