JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Elasticity & SHM

WhatsApp Email

The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is 10 s. If the metallic bob is immersed in water, then the new time period becomes

5 x

s. The value of

x

will be ______.

Answer: 5

Solution

When the bob is immersed in water, the effective gravity changes due to buoyant force.

Effective weight:

m g^{'} = m g - F_{B} = ρ_{B} V g - ρ_{w} V g

Effective gravity:

g^{'} = \frac{ρ _{B} - ρ _{w}}{ρ _{B}} \cdot g = \frac{5 - 1}{5} \cdot g = \frac{4 g}{5}

The time period ratio:

\frac{T ^{'}}{T} = \frac{g}{g ^{'}} = \frac{g}{4 g /5} = \frac{5}{4}

New time period:

T^{'} = T \frac{5}{4} = 10 \times \frac{5}{2} = 55

Comparing with

5 x

, we get

x = 5

JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Integer answer

Practise more: all JEE Main PYQs on Elasticity & SHM →

More JEE Main questions on Elasticity & SHM

Using a simple pendulum experiment g is determined by measuring its time period T. Which of the following plots represent the correct relation between the pendulum length L and time period T?
JEE Main 2026View solution →
The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of $176 rad / s$ . The frequency of this simple harmonic oscillator is___ Hz. $[$ take $π = \frac{22}{7}]$
JEE Main 2026View solution →
A simple pendulum of string length 30 cm performs 20 oscillations in 10 s. The length of the string required for the pendulum to perform 40 oscillations in the same time duration is ______ cm. [Assume that the mass of the pendulum remains same.]
JEE Main 2026View solution →
Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B as shown in figure. The energy stored in A is E. The energy stored in B, when spring constants $k_{A}$ , $k_{B}$ of A and B, respectively satisfy the relation $4 k_{A} = 3 k_{B}$ , is:
JEE Main 2026View solution →
The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus?
JEE Main 2026View solution →
A cylindrical block of mass M and area of cross section A is floating in a liquid of density $ρ$ and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is
JEE Main 2026View solution →