Two simple pendulums whose lengths are 1,m an | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{\ell}{g}}$.Let the length of the longer pendulum be $\ell_L = 121\,cm = 1.2

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(B) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{\ell}{g}}$.Let the length of the longer pendulum be $\ell_L = 121\,cm = 1.21\,m$ and the shorter pendulum be $\ell_S = 1\,m$.Let $N$ be the number of oscillations of the longer pendulum and $(N+1)$ be the number of oscillations of the shorter pendulum when they are in phase again.Since the total time taken is the same,we have $N \cdot T_L = (N+1) \cdot T_S$.Substituting the formula for $T$,we get $N \cdot 2\pi \sqrt{\frac{\ell_L}{g}} = (N+1) \cdot 2\pi \sqrt{\frac{\ell_S}{g}}$.$N \sqrt{\ell_L} = (N+1) \sqrt{\ell_S}$.Substituting the values: $N \sqrt{1.21} = (N+1) \sqrt{1}$.$1.1N = N + 1$.$0.1N = 1$.$N = 10$.Thus,the longer pendulum completes $10$ oscillations to be in phase with the shorter one.

Two simple pendulums whose lengths are $1\,m$ and $121\,cm$ are suspended side by side. Their bobs are pulled together and then released. After how many minimum oscillations of the longer pendulum will the two be in phase again?

Similar Questions

When the coordinate axes are rotated by an angle $\tan ^{-1}\left(\frac{3}{4}\right)$ about the origin,then the equation $x^2+y^2=9$ is transformed to the equation.

$A$ coil of wire of radius $r$ has $600$ turns and a self-inductance of $108 \ mH$. The self-inductance of a coil with the same radius and $500$ turns is: (in $mH$)

$1+\frac{2}{4}+\frac{2 \cdot 5}{4 \cdot 8}+\frac{2 \cdot 5 \cdot 8}{4 \cdot 8 \cdot 12}+\frac{2 \cdot 5 \cdot 8 \cdot 11}{4 \cdot 8 \cdot 12 \cdot 16}+\ldots \ldots$ is equal to :

The polar equation of the circle with centre $\left(2, \frac{\pi}{2}\right)$ and radius $3$ units is :

The correct order of dipole moment is

Vedclass Test Series

Exam Paper Generator

Online Exam Module