Question

Assertion :Due to anomalous behaviour of water, for the same mass, the volume of ice is more than that of water. Reason: When the temperature increases the length of the pendulum also increases and hence its time period increases. Thus it losses the time when temperature is increased

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are correct

Answer 1

The correct option is D Both Assertion and Reason are correct

Generally, the volume of substances increases on heating and decreases on cooling. But when water is heated from 0oC to 4oC, its volume decreases and increases only after 4oC. This unusual behaviour of water from 0oC to 4oC is known as anomalous expansion of water.

A pendulum clock keeps proper time at temperature ${\theta }_o$. If temperature is increased to $\theta (>{\theta }_o)$, then due to linear expansion, length of pendulum increases and hence its time period will increase.

Let $T=2\pi \sqrt{\frac{L_o}{g}}$ at temperature ${\theta }_o$

and $T^{\prime }=2\pi \sqrt{\frac{L^{\prime }}{g}}$ at temperature $\theta$

$\frac{T^{\prime }}{T}=\sqrt{\frac{L^{\prime }}{L}}=\sqrt{\frac{L(1+\alpha △\theta )}{L}}=1+\frac{1}{2}\alpha △\theta$

$\therefore$ change in time per unit time lapsed

$\frac{T^{\prime }-T}{T}=\frac{1}{2}\alpha △\theta$

Fractional change in time period $\frac{△T}{T}=\frac{1}{2}\alpha △\theta$

So, as the temperature increases, length of pendulum increases and hence time period of pendulum increases. Due to increment in its time period, a pendulum dock become slow in summer and will lose time.

Hence, Both Assertion and Reason are correct