Advertisements
Advertisements
Question
As the temperature is increased, the time period of a pendulum ______.
Options
increases as its effective length increases even though its centre of mass still remains at the centre of the bob.
decreases as its effective length increases even though its centre of mass still remains at the centre of the bob.
increases as its effective length increases due to shifting of centre of mass below the centre of the bob.
decreases as its effective length remains same but the centre of mass shifts above the centre of the bob.
Advertisements
Solution
As the temperature is increased, the time period of a pendulum increases as its effective length increases even though its centre of mass still remains at the centre of the bob.
Explanation:
A pendulum clock keeps proper time at temperature θ0. If the temperature is increased to θ (> θ0), then due to linear expansion, the length of pendulum increases and hence its time period will increase
Let T = `2πsqrt(L_0/g)` at temperature θ0
And T' = `2πsqrt(L/g)` at temperature θ.
`T^'/T = sqrt(L^'/L)`
= `sqrt((L[1 + αΔθ])/L`
= `1 + 1/2 αΔθ`
Therefore change (loss or gain) in time per unit time lapsed is `(T^' - T)/T = 1/2 αΔθ`
Fractional change in time period `(ΔT)/T = 1/2 αΔθ`
So, as the temperature increases, the length of pendulum increases and hence time period of the pendulum increases. Due to an increment in its time period, a pendulum clock becomes slow in summer and will lose time.
APPEARS IN
RELATED QUESTIONS
A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27.0 °C. What is the change in the diameter of the hole when the sheet is heated to 227 °C? Coefficient of linear expansion of copper = 1.70 × 10–5 K–1.
A 10 kW drilling machine is used to drill a bore in a small aluminium block of mass 8.0 kg. How much is the rise in temperature of the block in 2.5 minutes, assuming 50% of power is used up in heating the machine itself or lost to the surroundings Specific heat of aluminium = 0.91 J g–1 K–1
If mercury and glass had equal coefficients of volume expansion, could we make a mercury thermometer in a glass tube?
If an automobile engine is overheated, it is cooled by pouring water on it. It is advised that the water should be poured slowly with the engine running. Explain the reason.
A system X is neither in thermal equilibrium with Y nor with Z. The systems Y and Z
Answer the following question.
What is thermal stress?
Answer the following question.
Give an example of the disadvantages of thermal stress in practical use?
A glass flask has a volume 1 × 10−4 m3. It is filled with a liquid at 30°C. If the temperature of the system is raised to 100°C, how much of the liquid will overflow? (Coefficient of volume expansion of glass is 1.2 × 10−5 (°C)−1 while that of the liquid is 75 × 10−5 (°C)−1).
Solve the following problem.
In olden days, while laying the rails for trains, small gaps used to be left between the rail sections to allow for thermal expansion. Suppose the rails are laid at room temperature 27 °C. If maximum temperature in the region is 45 °C and the length of each rail section is 10 m, what should be the gap left given that α = 1.2 × 10–5K–1 for the material of the rail section?
A clock pendulum having coefficient of linear expansion. α = 9 × 10-7/°C-1 has a period of 0.5 s at 20°C. If the clock is used in a climate, where the temperature is 30°C, how much time does the clock lose in each oscillation? (g = constant)
A metal rod is heated to t°C. A metal rod has length, area of cross-section, Young's modulus and coefficient of linear expansion as 'L', 'A', 'Y' and 'a' respectively. When the rod is heated, the work performed is ______.
A metal rod of cross-sectional area 3 × 10-6 m2 is suspended vertically from one end has a length 0.4 m at 100°C. Now the rod is cooled upto 0°C, but prevented from contracting by attaching a mass 'm' at the lower end. The value of 'm' is ______.
(Y = 1011 N/m2, coefficient of linear expansion = 10-5/K, g = 10m/s2)
A bimetallic strip is made of aluminium and steel (αAl > αsteel) . On heating, the strip will ______.
A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly ______.
An aluminium sphere is dipped into water. Which of the following is true?
The height of mercury column measured with brass scale at temperature T0 is H0. What height H' will the mercury column have at T = 0°C. Coefficient of volume expansion of mercury is γ. Coefficient of linear expansion of brass is α ______.
A disc is rotating freely about its axis. The percentage change in angular velocity of a disc if temperature decreases by 20°C is ______.
(coefficient of linear expansion of material of disc is 5 × 10-4/°C)
The increase in the dimensions of a body due to an increase in its temperature is called ______.
The volume of a block of metal at 30°C changes by 0.12% when its temperature is increased to 70°C. The coefficient of linear expansion of the metal is ______.
