For the following questions answer them individually

Question 31

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?

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Question 32

A long solenoid of diameter 0.1 m has $$2 \times 10^4$$ turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is $$10 \pi^2 Ω$$, the total charge flowing through the coil during this time is

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Question 33

The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is

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Question 34

Suppose the charge of a proton and an electron differ slightly. One of them is -e, the other is $$(e + \triangle e)$$. If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then $$\triangle e$$ is of the order of [Given mass of hydrogen $$m_h = 1.67 \times 10^{-27}$$ kg]

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Question 35

The given electrical network is equivalent to

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Question 36

A Carnot engine having an efficiency of $$\frac{1}{10}$$ as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is

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Question 37

In an electromagnetic wave in free space the root mean square value of the electric field is $$E_rms = 6 V/m$$. The peak value of the magnetic field is

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Question 38

Two Polaroids $$P_1 and P_2$$ are placed with their axis perpendicular to each other. Unpolarised light $$I_0$$ is incident on $$P_1$$. A third polaroid $$P_3$$ is kept in between $$P_1 and P_2$$ such that its axis makes an angle $$45^\circ$$ with that of $$P_1$$. The intensity of transmitted light through $$P_2$$ is

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Question 39

If $$\theta_1 and \theta_2$$ be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip $$\theta$$ is given by

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Question 40

A 250-Turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of $$85 \mu A$$ and subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by $$180^\circ$$ against the torque is

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