Advertisements
Advertisements
प्रश्न
A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly ______.
विकल्प
its speed of rotation increases.
its speed of rotation decreases.
its speed of rotation remains same.
its speed increases because its moment of inertia increases.
Advertisements
उत्तर
A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly its speed of rotation decreases.
Explanation:
As the rod is heated, it expands. No external torque is acting on the system so angular momentum should be conserved.
L = Angular momentum = Iω = constant
⇒ I1ω1 = I2ω2
Due to the expansion of the rod I2 > I1
⇒ `ω_2/ω_1 = I_1/I_2 < 1`
⇒ `ω_2 < ω_1`
So, angular velocity (speed of rotation) decreases.
APPEARS IN
संबंधित प्रश्न
The coefficient of volume expansion of glycerin is 49 × 10–5 K–1. What is the fractional change in its density for a 30 °C rise in temperature?
If two bodies are in thermal equilibrium in one frame, will they be in thermal equilibrium in all frames?
The density of water at 0°C is 0.998 g cm–3 and at 4°C is 1.000 g cm–1. Calculate the average coefficient of volume expansion of water in the temperature range of 0 to 4°C.
A steel rod is clamped at its two ends and rests on a fixed horizontal base. The rod is unstrained at 20°C.
Find the longitudinal strain developed in the rod if the temperature rises to 50°C. Coefficient of linear expansion of steel = 1.2 × 10–5 °C–1.
Show that the moment of inertia of a solid body of any shape changes with temperature as I = I0 (1 + 2αθ), where I0 is the moment of inertia at 0°C and α is the coefficient of linear expansion of the solid.
Answer the following question.
Derive the relation between three coefficients of thermal expansion.
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?
An iron plate has a circular hole of a diameter 11 cm. Find the diameter of the hole when the plate is uniformly heated from 10° C to 90° C.`[alpha = 12 xx 10^-6//°"C"]`
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 hot body at a temperature 'T' is kept in a surrounding of temperature 'T0'. It takes time 't1' to cool from 'T' to 'T2', time t2 to cool from 'T2' to 'T3' and time 't3' to cool from 'T3' to 'T4'. If (T - T2) = (T2 - T3) = (T3 - T4), then ______.
The volume of a metal block changes by 0.86% when heated through 200 °C then its coefficient of cubical expansion is ______.
A bimetallic strip is made of aluminium and steel (αAl > αsteel) . On heating, the strip will ______.
The radius of a metal sphere at room temperature T is R, and the coefficient of linear expansion of the metal is α. The sphere is heated a little by a temperature ∆T so that its new temperature is T + ∆T. The increase in the volume of the sphere is approximately ______.
Find out the increase in moment of inertia I of a uniform rod (coefficient of linear expansion α) about its perpendicular bisector when its temperature is slightly increased by ∆T.
Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of 57°C is drunk. You can take body (tooth) temperature to be 37°C and α = 1.7 × 10–5/°C, bulk modulus for copper = 140 × 109 N/m2.
A rail track made of steel having length 10 m is clamped on a raillway line at its two ends (figure). On a summer day due to rise in temperature by 20° C, it is deformed as shown in figure. Find x (displacement of the centre) if αsteel = 1.2 × 10–5/°C.
A metal ball immersed in water weighs w1 at 0°C and w2 at 50°C. The coefficient of cubical expansion of metal is less than that of water. Then ______.
When a solid is heated, its atoms vibrate faster and move farther apart. This happens because ______.
