Vertical Circular Motion

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JEE Main 2021

LEVELJEE Main

A pendulum bob has a speed of $3 m/s$ at its lowest position. The pendulum is $50 cm$ long. The speed of bob when the length makes an angle of $6 0^{\circ}$ to the vertical will be ....... $m/s$ . (Take, $g = 10 m/s^{2}$ )

JEE Main 2021, 25 Feb Shift-I

LEVELJEE Advanced

A small bob tied at one end of a thin string of length 1m is describing a vertical circle, so that the maximum and minimum tension in the string are in the ratio 5 : 1. The velocity of the bob at the highest position is ……… m/s. (Take, $g = 10 m/s^{2}$ )

JEE Main 2021, 27 July Shift-II

LEVELJEE Advanced

A small block slides down from the top of hemisphere of radius $R = 3$ m as shown in the figure. The height $h$ at which the block will lose contact with the surface of the sphere is ………… m. (Assume there is no friction between the block and the hemisphere)

JEE Main 2021, 27 Aug Shift-II

LEVELJEE Advanced

A bullet of $10 g$ , moving with velocity $v$ , collides head-on with the stationary bob of a pendulum and recoils with velocity $100 m/s$ . The length of the pendulum is $0.5 m$ and mass of the bob is $1 kg$ . The minimum value of $v$ .......... $m/s$ , so that the pendulum describes a circle. (Assume, the string to be inextensible and $g = 10 m/s^{2}$ )

JEE Advanced 2013

LEVELJEE Advanced

A bob of mass $m$ , suspended by a string of length $l_{1}$ , is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass $m$ suspended by a string of length $l_{2}$ , which is initially at rest. Both the strings are massless and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio $l_{1} / l_{2}$ is

JEE Advanced (2008)

LEVELJEE Advanced

A bob of mass $M$ is suspended by a massless string of length $L$ . The horizontal velocity $v$ at position $A$ is just sufficient to make it reach the point $B$ . The angle $θ$ at which the speed of the bob is half of that at $A$ , satisfies

(A)

θ = \frac{π}{4}

(B)

\frac{π}{4} < θ < \frac{π}{2}

(C)

\frac{π}{2} < θ < \frac{3 π}{4}

(D)

\frac{3 π}{4} < θ < π

JEE Advanced (1999)

LEVELJEE Advanced

A particle is suspended vertically from a point $O$ by an inextensible massless string of length $L$ . A vertical line $A B$ is at a distance $L /8$ from $O$ as shown in figure. The object is given a horizontal velocity $u$ . At some point, its motion ceases to be circular and eventually the object passes through the line $A B$ . At the instant of crossing $A B$ , its velocity is horizontal. Find $u$ .

JEE Advanced 1998

LEVELJEE Main

A stone tied to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position, and has a speed $u$ . The magnitude of the change in its velocity as it reaches a position, where the string is horizontal, is

(A)

u^{2} - 2 g L

(B)

2 g L

(C)

u^{2} - g L

(D)

2 (u^{2} - g L)

JEE Advanced 1988

LEVELJEE Advanced

A bullet of mass $M$ is fired with a velocity $50 m/s$ at an angle $θ$ with the horizontal. At the highest point of its trajectory, it collides head-on with a bob of mass $3 M$ suspended by a massless string of length $10/3 m$ and gets embedded in the bob. After the collision, the string moves through an angle of $12 0^{\circ}$ . Find (a) the angle $θ$ , (b) the vertical and horizontal coordinates of the initial position of the bob with respect to the point of firing of the bullet. (Take $g = 10 m/s^{2}$ )

JEE Advanced 2002

LEVELJEE Advanced

A spherical ball of mass $m$ is kept at the highest point in the space between two fixed, concentric spheres $A$ and $B$ (see fig.). The smaller sphere $A$ has a radius $R$ and the space between the two spheres has a width $d$ . The ball has a diameter very slightly less than $d$ . All surfaces are frictionless. The ball is given a gentle push (towards the right in the figure). The angle made by the radius vector of the ball with the upward vertical is denoted by $θ$ . (a) Express the total normal reaction force exerted by the spheres on the ball as a function of angle $θ$ . (b) Let $N_{A}$ and $N_{B}$ denote the magnitudes of the normal reaction forces on the ball exerted by the spheres $A$ and $B$ , respectively. Sketch the variations of $N_{A}$ and $N_{B}$ as function of $cos θ$ in the range $0 \leq θ \leq π$ by drawing two separate graphs in your answer book, taking $cos θ$ on the horizontal axis.

JEE Advanced 2014

LEVELJEE Advanced

A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is

(A)

Always radially outwards

(B)

Always radially inwards

(C)

Radially outwards initially and radially inwards later.

(D)

Radially inwards initially and radially outwards later.