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A pendulum clock loses 12 s a day if the temperature is 40 °C and gains 4 s in a day if the temperature is 20 °C. The temperature at which the clock will show correct time and the coefficient of linear expansion α of the metal of the pendulum shaft are, respectively.

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Important Questions on JEE Advanced 2016 (Solved)

EASY
JEE Main
IMPORTANT
An ideal gas undergoes a quasi-static reversible process in which its molar heat capacity C remains constant. If during this process, the relation of pressure p and volume V is given by pVn=constant, then n is given by (here Cp and CV are molar specific heat at constant pressure and constant volume, respectively.)
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JEE Main
IMPORTANT

n moles of an ideal gas undergoes a process A and B as shown in the figure. The maximum temperature of the gas during the process will be,

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MEDIUM
JEE Main
IMPORTANT
A particle performs simple harmonic motion with amplitude A. Its speed is trebled at the instant that it is at a distance 23A from equilibrium position. The new amplitude of the motion is
MEDIUM
JEE Main
IMPORTANT
A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is (Take, g=10 m s-2)
MEDIUM
JEE Main
IMPORTANT
A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions are used to measure the thickness of a thin sheet of aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet, if the main scale reading is 0.5 mm and the 25 th division coincides with the main scale line?
EASY
JEE Main
IMPORTANT
A pipe open at both ends has a fundamental frequency f in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now
HARD
JEE Main
IMPORTANT

A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly 3 kW of heat (thermal load). The temperature of water fed into the device cannot exceed 30 °C and the entire stored 120 litres of water is initially cooled to 10 °C. The entire system is thermally insulated. The minimum value of P (in watts) for which the device can be operated for 3 hours  is

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(specific heat of water is 4.2 kJ kg-1 K-1 and the density of water is 1000 kg m-3).

HARD
JEE Main
IMPORTANT
A uniform wooden stick of mass 1.6 kg of length l rests in an inclined manner on a smooth, vertical wall of height h<l such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of 30° with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. The ratio hl and the frictional force f at the bottom of the stick are g=10 m s-2