The time period of a simple pendulum is T. Wh | vedclass

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

Question

(C) The time period of a simple pendulum is given by $T = 2 \pi \sqrt{\frac{l}{g}}$,so $T^2 = 4 \pi^2 \frac{l}{g} \quad \dots (i)$When the length is i

Vedclass · Accepted Answer

$2 T^2 = T_1^2 + T_2^2$

Vedclass · Answer

(C) The time period of a simple pendulum is given by $T = 2 \pi \sqrt{\frac{l}{g}}$,so $T^2 = 4 \pi^2 \frac{l}{g} \quad \dots (i)$When the length is increased by $10 \ cm$,the new time period $T_1$ is given by $T_1^2 = 4 \pi^2 \frac{(l + 10)}{g} \quad \dots (ii)$When the length is decreased by $10 \ cm$,the new time period $T_2$ is given by $T_2^2 = 4 \pi^2 \frac{(l - 10)}{g} \quad \dots (iii)$Adding equations $(ii)$ and $(iii)$,we get$T_1^2 + T_2^2 = 4 \pi^2 \left[ \frac{l + 10}{g} + \frac{l - 10}{g} \right]$$T_1^2 + T_2^2 = 4 \pi^2 \left[ \frac{2l}{g} \right]$$T_1^2 + T_2^2 = 2 \left( 4 \pi^2 \frac{l}{g} \right)$Since $T^2 = 4 \pi^2 \frac{l}{g}$,we have$T_1^2 + T_2^2 = 2 T^2$

The time period of a simple pendulum is $T$. When the length is increased by $10 \ cm$,its period is $T_1$. When the length is decreased by $10 \ cm$,its period is $T_2$. Then,the relation between $T, T_1$ and $T_2$ is

Similar Questions

The area (in sq. units) of the triangle formed by the tangent and the normal at the point $\left(\frac{a}{\sqrt{2}}, \frac{b}{\sqrt{2}}\right)$ to the curve $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and the $X$-axis is

The distance of the point $(1, 1, 9)$ from the point of intersection of the line $\frac{x-3}{1} = \frac{y-4}{2} = \frac{z-5}{2}$ and the plane $x+y+z=17$ is

If $x$ is a solution of the equation $\sqrt{2x+1} - \sqrt{2x-1} = 1$ for $x \geq \frac{1}{2}$,then $\sqrt{4x^2-1}$ is equal to:

Steam at $100\,^{\circ}C$ is passed into $1.1\,kg$ of water contained in a calorimeter of water equivalent $0.02\,kg$ at $15\,^{\circ}C$ until the temperature of the calorimeter rises to $80\,^{\circ}C$. The mass of steam condensed in kilograms is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module