A pendulume clock loses 12s a day if temperature is 40^oC and gains 4s a day if temperature is 20^oC

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13.Oscillations

hard

A pendulume clock loses $12\;s$ a day if the temperature is $40^oC$ and gains $4\;s$ a day if the temperature is $20^oC$. The temperature at which the clock will show correct time, and the coeffecient of linear expansion $(\alpha)$ of the metal of the pendulum shaft are respectively

$30^o $ $C$ ,$\;\alpha $ $= 1.85 \times 10^{-3}/^o C$

$55^o C$ ,$\;\alpha $ $= 1.85 \times 10^{-2}/^o C$

$25^o C$ ,$\;\alpha $$ = 1.85 \times 10^{-5}/^o C$

$60^o $ $C$ ,$\;\alpha $ = $1.85 \times10^{-4}/^o C$

(JEE MAIN-2016)

Solution

$\mathrm{T}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}}}$

$\frac{\Delta \mathrm{T}}{\mathrm{T}}=\frac{1}{2} \frac{\Delta \ell}{\ell}$

When clock gain $12\, sec$

$\frac{12}{\mathrm{T}}=\frac{1}{2} \alpha(40-\theta)$ $…(1)$

When clock lose $4\, sec.$

$\frac{4}{\mathrm{T}}=\frac{1}{2} \alpha(\theta-20)$ $…(2)$

From equation $( 1)\&(2)$

$3=\frac{40-\theta}{\theta-20}$

$3 \theta-60=40-\theta$

$4 \theta=100$

$\theta=25^{\circ} \mathrm{C}$

from equation $( 1 )$

$\frac{12}{\mathrm{T}}=\frac{1}{2} \alpha(40-25)$

$\frac{12}{24 \times 3600}=\frac{1}{2} \alpha \times 15$

$\alpha=\frac{24}{24 \times 3600 \times 15}$

$\alpha=1.85 \times 10^{-15} /^{\circ} \mathrm{C}$

Standard 11

Physics

If the mass of a bob of a pendulum increased by $9$ times, the period of pendulum will ?

easy

A simple pendulum is released from rest at the horizontally stretched position. When the string makes an angle $\theta$ with the vertical, the angle $\phi$ which the acceleration vector of the bob makes with the string is given by

hard

(KVPY-2012)

In the following table relation of graph in column$-I$ and shape of graph in column$-II$ is shown match them appropriately.

column$-I$ column $-II$

$(a)$ ${T^2} \to l$ $(i)$ Linear

$(b)$ ${T^2} \to g$ $(ii)$ Parabolic

$(c)$ ${T} \to l$ $(iii)$ Hyperbolic

medium

At which position in the string of simple pendulum has maximum tension ?

easy

lfa simple pendulum has significant amplitude (up to a factor of $1/e$ of original) only in the period between $t = 0\ s$ to $t = \tau \ s$, then $\tau$ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation ( due to viscous drag) proportional to its velocity with $b$ as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds

hard

(AIEEE-2012)

column$-I$	column $-II$
$(a)$ ${T^2} \to l$	$(i)$ Linear
$(b)$ ${T^2} \to g$	$(ii)$ Parabolic
$(c)$ ${T} \to l$	$(iii)$ Hyperbolic

A pendulume clock loses $12\;s$ a day if the temperature is $40^oC$ and gains $4\;s$ a day if the temperature is $20^oC$. The temperature at which the clock will show correct time, and the coeffecient of linear expansion $(\alpha)$ of the metal of the pendulum shaft are respectively

Solution

Similar Questions

If the mass of a bob of a pendulum increased by $9$ times, the period of pendulum will ?

A simple pendulum is released from rest at the horizontally stretched position. When the string makes an angle $\theta$ with the vertical, the angle $\phi$ which the acceleration vector of the bob makes with the string is given by

In the following table relation of graph in column$-I$ and shape of graph in column$-II$ is shown match them appropriately. column$-I$ column $-II$ $(a)$ ${T^2} \to l$ $(i)$ Linear $(b)$ ${T^2} \to g$ $(ii)$ Parabolic $(c)$ ${T} \to l$ $(iii)$ Hyperbolic

At which position in the string of simple pendulum has maximum tension ?

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In the following table relation of graph in column$-I$ and shape of graph in column$-II$ is shown match them appropriately.

column$-I$ column $-II$

$(a)$ ${T^2} \to l$ $(i)$ Linear

$(b)$ ${T^2} \to g$ $(ii)$ Parabolic

$(c)$ ${T} \to l$ $(iii)$ Hyperbolic