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A metal ball of mass 1 kg is heated by means of a 20 W heater in a room at 20°C. The temperature of the ball becomes steady at 50°C. (a) Find the rate of loss of heat to the surrounding when the ball is at 50°C. (b) Assuming Newton's law of cooling, calculate the rate of loss of heat to the surrounding when the ball rises 30°C. (c) Assume that the temperature of the ball rises uniformly from 20°C to 30°C in 5 minutes. Find the total loss of heat to the surrounding during this period. (d) Calculate the specific heat capacity of the metal.
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A hot body placed in a surrounding of temperature θ0 obeys Newton's law of cooling `(d theta)/(dt) = -K(theta - theta_0)` . Its temperature at t = 0 is θ1. The specific heat capacity of the body is sand its mass is m. Find (a) the maximum heat that the body can lose and (b) the time starting from t = 0 in which it will lose 90% of this maximum heat.
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Which of the following is not a unit of time?
- Second
- Parsec
- Year
- Light year
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An astronaut inside a small spaceship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size, can he hope to detect gravity?
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A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plot shown in figure, indicate the one that represents the velocity (v) of the pebble as a function of time (t).
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Consider a Carnot’s cycle operating between T1 = 500 K and T2 = 300 K producing 1 k J of mechanical work per cycle. Find the heat transferred to the engine by the reservoirs.
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In a refrigerator one removes heat from a lower temperature and deposits to the surroundings at a higher temperature. In this process, mechanical work has to be done, which is provided by an electric motor. If the motor is of 1 kW power, and heat is transferred from – 3°C to 27°C, find the heat taken out of the refrigerator per second assuming its efficiency is 50% of a perfect engine.
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A vessel of volume V contains a mixture of 1 mole of Hydrogen and 1 mole of Oxygen (both considered as ideal). Let f1(v)dv, denote the fraction of molecules with speed between v and (v + dv) with f2(v)dv, similarly for oxygen. Then ______.
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Consider an ideal gas with following distribution of speeds.
| Speed (m/s) | % of molecules |
| 200 | 10 |
| 400 | 20 |
| 600 | 40 |
| 800 | 20 |
| 1000 | 10 |
Calculate Vrms and hence T. (m = 3.0 × 10−26 kg)
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Consider an ideal gas with following distribution of speeds.
| Speed (m/s) | % of molecules |
| 20 | 10 |
| 400 | 20 |
| 600 | 40 |
| 800 | 20 |
| 1000 | 10 |
If all the molecules with speed 1000 m/s escape from the system, calculate new Vrms and hence T.
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A man stands on a rotating platform, with his arms stretched horizontally holding a 5 kg weight in each hand. The angular speed of the platform is 30 revolutions per minute. The man then brings his arms close to his body with the distance of each weight from the axis changing from 90cm to 20cm. The moment of inertia of the man together with the platform may be taken to be constant and equal to 7.6 kg m2.
(a) What is his new angular speed? (Neglect friction.)
(b) Is kinetic energy conserved in the process? If not, from where does the change come about?
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A ball is whirled in a circle by attaching it to a fixed point with a string. Is there an angular rotation of the ball about its centre? If yes, is this angular velocity equal to the angular velocity of the ball about the fixed point?
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If the angular momentum of a body is found to be zero about a point, is it necessary that it will also be zero about a different point?
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A body is uniformly rotating about an axis fixed in an inertial frame of reference. Let \[\overrightarrow A\] be a unit vector along the axis of rotation and \[\overrightarrow B\] be the unit vector along the resultant force on a particle P of the body away from the axis. The value of \[\overrightarrow A.\overrightarrow B\] is _________.
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A particle moves with a constant velocity parallel to the X-axis. Its angular momentum with respect to the origin ____________.
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A person sitting firmly over a rotating stool has his arms stretched. If he folds his arms, his angular momentum about the axis of rotation ___________ .
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A particle moves on a straight line with a uniform velocity. Its angular momentum __________ .
(a) is always zero
(b) is zero about a point on the straight line
(c) is not zero about a point away from the straight line
(d) about any given point remains constant.
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If there is no external force acting on a nonrigid body, which of the following quantities must remain constant?
(a) angular momentum
(b) linear momentum
(c) kinetic energy
(d) moment of inertia.
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A wheel rotating with uniform angular acceleration covers 50 revolutions in the first five seconds after the start. Find the angular acceleration and the angular velocity at the end of five seconds.
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A disc rotates about its axis with a constant angular acceleration of 4 rad/s2. Find the radial and tangential accelerations of a particle at a distance of 1 cm from the axis at the end of the first second after the disc starts rotating.
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