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 $= 4 mg$

  • A
    $P-1, Q-2, R-3, S-4$
  • B
    $P-4, Q-2, R-3, S-1$
  • C
    $P-1, Q-3, R-2, S-4$
  • D
    $P-4, Q-3, R-2, S-1$

Explore More

Similar Questions

$A$ particle of mass $m$ is released from a height $H$ on a smooth curved surface which ends into a vertical loop of radius $R$,as shown. If $\theta$ is the instantaneous angle which the line joining the particle and the centre of the loop makes with the vertical,then identify the correct statement$(s)$ related to the normal reaction $N$ between the block and the surface.

What will be the minimum speed of the roller-coaster so that the passenger at the top, when becomes upside down, does not fall out (in $m \ s^{-1}$)? Consider the acceleration due to gravity as $10 \ m \ s^{-2}$, and the radius of curvature of the roller coaster is $10 \ m$.

$A$ block follows the path as shown in the figure from height $h$. If the radius of the circular path is $r$,then the relation that holds good to complete a full circle is

$A$ stone of mass $m$ tied to the end of a string revolves in a vertical circle of radius $R$. The net forces at the lowest and highest points of the circle directed vertically downwards are:
Lowest PointHighest Point
$(a) \ mg - T_1$$mg + T_2$
$(b) \ mg + T_1$$mg - T_2$
$(c) \ mg + T_1 - \frac{mv_1^2}{R}$$mg - T_2 + \frac{mv_2^2}{R}$
$(d) \ mg - T_1 - \frac{mv_1^2}{R}$$mg + T_2 + \frac{mv_2^2}{R}$

$T_1$ and $v_1$ denote the tension and speed at the lowest point. $T_2$ and $v_2$ denote corresponding values at the highest point.

$A$ bucket filled with water is tied to a rope of length $0.5 \,m$ and is rotated in a circular path in a vertical plane. The minimum velocity it should have at the lowest point of the circle so that the water does not spill is, $(g=10 \,m/s^2)$

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo