T is the time period of a simple pendulum on | 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 $T = 2\pi \sqrt{\frac{\ell}{g}}$,where $g$ is the acceleration due to gravity at the surface.At a

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{\ell}{g}}$,where $g$ is the acceleration due to gravity at the surface.At a height $h = R$ above the surface,the acceleration due to gravity $g'$ is given by $g' = \frac{g}{(1 + h/R)^2}$.Substituting $h = R$,we get $g' = \frac{g}{(1 + R/R)^2} = \frac{g}{(2)^2} = \frac{g}{4}$.The new time period $T'$ is $T' = 2\pi \sqrt{\frac{\ell}{g'}} = 2\pi \sqrt{\frac{\ell}{g/4}} = 2 	imes 2\pi \sqrt{\frac{\ell}{g}} = 2T$.Given that the new time period is $xT$,we have $xT = 2T$,which implies $x = 2$.

$T$ is the time period of a simple pendulum on the Earth's surface. Its time period becomes $xT$ when taken to a height $R$ (equal to the Earth's radius) above the Earth's surface. Then,the value of $x$ will be:

Similar Questions

Acceleration due to gravity at a height $h$ is equal to that at a depth $d$ below the surface of the earth,if

$R$ is the radius of the Earth,$\omega$ is its angular velocity,and $g_p$ is the value of acceleration due to gravity at the poles. The effective value of $g$ at latitude $\lambda = 60^\circ$ will be equal to:

What is the acceleration due to gravity at a distance of $2R$ from the surface of the Earth,where $R$ is the radius of the Earth?

Let $g$ be the acceleration due to gravity at the Earth's surface and $K$ be the rotational kinetic energy of the Earth. Suppose the Earth's radius decreases by $2 \%$ keeping its mass the same,then:

The gravitational pull of the moon is $(1/6)^{\text{th}}$ of the earth and the mass of the moon is $(1/8)^{\text{th}}$ of the earth. This implies that the:

Vedclass Test Series

Exam Paper Generator

Online Exam Module