A uniform metal rod is used as a bar pendulum | vedclass

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

Question

(D) The time period of a simple pendulum is given by $T = 2 \pi \sqrt{\frac{L}{g}}$.For a bar pendulum,the effective length $L$ is proportional to the

Vedclass · Accepted Answer

$1 	imes 10^{-3} \%$

Vedclass · Answer

(D) The time period of a simple pendulum is given by $T = 2 \pi \sqrt{\frac{L}{g}}$.For a bar pendulum,the effective length $L$ is proportional to the length of the rod.Taking the natural logarithm and differentiating,we get $\frac{\Delta T}{T} = \frac{1}{2} \frac{\Delta L}{L}$.Since $\Delta L = L \alpha \Delta 	heta$,we have $\frac{\Delta L}{L} = \alpha \Delta 	heta$.Substituting this into the expression for the fractional change in time period: $\frac{\Delta T}{T} = \frac{1}{2} \alpha \Delta 	heta$.Given $\alpha = 2 	imes 10^{-6} /^{\circ} C$ and $\Delta 	heta = 10^{\circ} C$,we calculate:$\frac{\Delta T}{T} = \frac{1}{2} 	imes (2 	imes 10^{-6}) 	imes 10 = 10^{-5}$.The percentage increase is $\frac{\Delta T}{T} 	imes 100 = 10^{-5} 	imes 100 = 10^{-3} \%$.

$A$ uniform metal rod is used as a bar pendulum. If the room temperature rises by $10^{\circ} C$ and the coefficient of linear expansion of the metal of the rod is $2 \times 10^{-6} /^{\circ} C$,the period of the pendulum will have a percentage increase of

Similar Questions

If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors and $\lambda$ is a real number,then the vectors $\vec{a}+2 \vec{b}+3 \vec{c}$,$\lambda \vec{b}+4 \vec{c}$,and $(2 \lambda-1) \vec{c}$ are non-coplanar for:

The locus of $z$ satisfying the inequality $\left|\frac{z+2 i}{2 z+i}\right| < 1$,where $z=x+i y$,is

$5$ moles of Hydrogen $\left(\gamma=\frac{7}{5}\right)$ initially at $S.T.P.$ are compressed adiabatically so that its temperature becomes $400^{\circ} C$. The increase in the internal energy of the gas in kilo-joules is $(R=8.30 \ J \ mol^{-1} \ K^{-1})$.

Which of the following elements shows a stable $+2$ oxidation state?

Velocity and acceleration vectors of a charged particle moving perpendicular to the direction of a magnetic field at a given instant of time are $\overrightarrow{v}=2 \hat{i}+c \hat{j}$ and $\overrightarrow{a}=3 \hat{i}+4 \hat{j}$ respectively. Then the value of $c$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module