11.

Helium gas goes through a cycle ABCDA (consisting of two isochoric and two isobaric lines) as shown in the figure. Efficiency of this cycle is nearly:(Assume the gas to be close to ideal gas)

• 15.4%

• 9.1%

• 10.5%

• 10.5%

If a simple pendulum has the significant amplitude (up to a factor of 1/e of original) only in the period between t = Os to t = τs, then τ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with 'b' as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds:

• 0.693/b

• b

• 1/b

• 1/b

A wooden wheel of radius R is made of two semicircular parts (see figure); The two parts are held together by a ring made of a metal strip of cross sectional area S and length L. L is slightly less than 2πR. To fit the ring on the wheel, it is heated so that it temperature rises by ∆T and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is α, and its Youngs'modulus is Y, the force that one part of the wheel applies on the other part is :

• 2πSYα∆T

• SYα∆T

• πSYα ∆T

• πSYα ∆T

This question has statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.
An insulating solid sphere of radius R has a uniformly positive charge density ρ. As a result of this uniform charge distribution, there is a finite value of the electric potential at the centre of the sphere, at the
surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero.

Statement 1: When a charge q is taken from the centre to the surface of the sphere, its potential energy changes by qρ/3ε_o
Statement 2: The electric field at a distance r(r < R) from the centre of the sphere is  ρr/3ε_o

• Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for statement 1.

• Statement 1 is true, Statement 2 is false

• Statement 1 is false, Statement 2 is true

• Statement 1 is false, Statement 2 is true

The resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is

• 6%

• zero

• 1%

• 1%

Two electric bulbs marked 25W – 220V and 100W – 220V are connected in series to a 440Vsupply. Which of the bulbs will fuse?

• Both

• 100 W

• 25 W

• 25 W

A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating; it is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to

• development of air current when the plate is placed.

• induction of electrical charge on the plate

• shielding of magnetic lines of force as aluminium is a paramagnetic material.

• shielding of magnetic lines of force as aluminium is a paramagnetic material.

An electromagnetic wave in vaccum has the electric and magnetic fields  and which are always perpendicular to each other. the direction of polarisation is given by  and that of wave propagation by  then

In a uniformly charged sphere of total charge Q and radius R, the electric field E is plotted as a function of distance from the centre. The graph which would correspond to the above will be

The figure shows an experimental plot for discharging of a capacitor in an R-C circuit. The time constant τ of this circuit lies between

• 150 sec and 200 sec

• 0 and 50 sec

• 50 sec and 100 sec

• 50 sec and 100 sec