JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Work, Power & Energy

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

(g = 10 m / s^{2})

____

m / s

Answer: 2

Solution

Using conservation of energy between lowest position and position at angle

60°

\frac{1}{2} m v_{0}^{2} = \frac{1}{2} m v^{2} + m g h

where

h = L (1 - cos 60°) = 0.5 (1 - 0.5) = 0.25

\frac{1}{2} (3)^{2} = \frac{1}{2} v^{2} + 10 \times 0.25

4.5 = \frac{1}{2} v^{2} + 2.5

\frac{1}{2} v^{2} = 2

v^{2} = 4

v = 2 m / s

JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Numerical answer

Practise more: all JEE Main PYQs on Work, Power & Energy →

More JEE Main questions on Work, Power & Energy

Given below are two statements:
Statement I: An object moves from position $r_{1}$ to position $r_{2}$ under a conservative force field $F$ . The work done by the force is $W = - \int_{r_{1}}^{r_{2}} F \cdot d r$ .
Statement II: Any object moving from one l …
JEE Main 2026View solution →
Consider two identical metallic spheres of radius $R$ each having charge $Q$ and mass $m$ . Their centers have an initial separation of $4 R$ . Both the spheres are given an initial speed of $u$ towards each other. The minimum value of $u$ , so that they can just touch e …
JEE Main 2026View solution →
A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by $x (t) = α t^{2} + β t + γ m$ , where $α = 1 m / s^{2}$ , $β = 1 m / s$ an …
JEE Main 2026View solution →
In case of vertical circular motion of a particle by a thread of length r if the tension in the thread is zero at an angle 30° shown in figure, the velocity at the bottom point (A) of the circular path is (g = gravitational acceleration)
JEE Main 2026View solution →
A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average force exerted by sand on the ball is $____$ N.
JEE Main 2026View solution →
A 1 kg block subjected to two simultaneous forces $(2 \hat{i} + 3 \hat{j} + 4 \hat{k})$ N and $(3 \hat{i} - \hat{j} - 2 \hat{k})$ N is moved a distance of 25 m along $(3 \hat{i} - 4 \hat{j})$ direction. The work done in this process is _____ J.
JEE Main 2026View solution →