PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions

The specific heat capacities of hydrogen at constant volume and at constant pressure are 2.4 cal g⁻¹ °C⁻¹ and 3.4 cal g⁻¹ °C⁻¹ respectively. The molecular weight of hydrogen is 2 g mol⁻¹ and the gas constant, R = 8.3 × 10⁷ erg °C⁻¹ mol⁻¹. Calculate the value of J.

The normal body-temperature of a person is 97°F. Calculate the rate at which heat is flowing out of his body through the clothes assuming the following values. Room temperature = 47°F, surface of the body under clothes = 1.6 m², conductivity of the cloth = 0.04 J s⁻¹ m⁻¹°C⁻¹, thickness of the cloth = 0.5 cm.

A cubical block of mass 1.0 kg and edge 5.0 cm is heated to 227°C. It is kept in an evacuated chamber maintained at 27°C. Assuming that the block emits radiation like a blackbody, find the rate at which the temperature of the block will decrease. Specific heat capacity of the material of the block is 400 J Kg^-1 K-^1.

A copper sphere is suspended in an evacuated chamber maintained at 300 K. The sphere is maintained at a constant temperature of 500 K by heating it electrically. A total of 210 W of electric power is needed to do it. When the surface of the copper sphere is completely blackened, 700 W is needed to maintain the same temperature of the sphere. Calculate the emissivity of copper.

One end of a rod of length 20 cm is inserted in a furnace at 800 K. The sides of the rod are covered with an insulating material and the other end emits radiation like a blackbody. The temperature of this end is 750 K in the steady state. The temperature of the surrounding air is 300 K. Assuming radiation to be the only important mode of energy transfer between the surrounding and the open end of the rod, find the thermal conductivity of the rod. Stefan constant σ = 6.0 × 10⁻⁸ W m⁻² K⁻⁴.

A body cools down from 50°C to 45°C in 5 mintues and to 40°C in another 8 minutes. Find the temperature of the surrounding.

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.

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.

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?

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?

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 _________.

A particle moves with a constant velocity parallel to the X-axis. Its angular momentum with respect to the origin ____________.

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 ___________ .

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.

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.

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.

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.

A uniform square plate of mass 2⋅0 kg and edge 10 cm rotates about one of its diagonals under the action of a constant torque of 0⋅10 N-m. Calculate the angular momentum and the kinetic energy of the plate at the end of the fifth second after the start.

Calculate the ratio of the angular momentum of the earth about its axis due to its spinning motion to that about the sun due to its orbital motion. Radius of the earth = 6400 km and radius of the orbit of the earth about the sun = 1⋅5 × 10⁸ km.

Two particles of masses m₁ and m₂ are joined by a light rigid rod of length r. The system rotates at an angular speed ω about an axis through the centre of mass of the system and perpendicular to the rod. Show that the angular momentum of the system is \[L = \mu r^2 \omega\] where \[\mu\] is the reduced mass of the system defined as \[\mu = \frac{m_1 + m_2}{m_1 + m_2}\]