If ΔU and ΔW represent the increase in internal energy and work done by the system respectively in a thermodynamical process, which of the following is true?

ΔU = -ΔW,in an adiabatic process
ΔU = ΔW,in an isothermal process
ΔU = ΔW,in an adiabatic process
ΔU = -ΔW,in an isothermal process

Solution

By first law of thermodynamics,

ΔQ = ΔU + ΔW

In adiabatic process, ΔQ = 0

∴ ΔU = -ΔW

In isothermal process, ΔU = 0

∴ ΔQ = ΔW

Let A= iA cos θ+ jA sin θ be any vector. Another vector B,which is normal to A can be expressed as

i B cos θ– j B sin θ
i B cos θ+ j B sin θ
i B sin θ– j B cos θ
i B sin θ+ j B cos θ

Solution

The dot product should be zero.

A cylinder rolls down an inclined plane of inclination 30°,the acceleration of cylinder is

^g⁄₃
g
^g⁄₂
^2g⁄₃

Solution

Two points separated by a distance of 0.1 mm can just be inspected in a microscope, when light of wavelength 600 Å is used. If the light of wavelength 4800 Å is used, the limit of resolution will become

0.80 mm
0.12 mm
0.10 mm
0.08 mm

Solution

A glass marble dropped from a certain height above the horizontal surface reaches the surface in time t and then continues to bounce up and down. The time in which the marble finally comes to rest is

eⁿt
e²t
\(t\left [ \frac{1+e}{1-e} \right ]\)
\(t\left [ \frac{1-e}{1+e} \right ]\)

Solution

The displacement of particle is given by \(x=a_{0}+\frac{a_{1}t}{2}-\frac{a_{2}t^{2}}{3}\). What is its acceleration?

\(\frac{2a_{2}}{3}\)
\(-\frac{2a_{2}}{3}\)
a₂
zero

Solution

If a current increases from zero to one ampere in 0.1 second in a coil of 5 mH, then the magnitude of the induced e.m.f.will be

0.005 volt
0.5 volt
0.05 volt
5 volt

Solution

ε = (5 × 10^-3)(1/ 0.1) = 0.05V.

The relative permeability of a medium is 0.075. What is its magnetic susceptibility?

0.925
– 0.925
1.075
–1.075

Solution

From μ_rr = 1 + x_m;

Magnetic suscaptibility, x_m = μ_rr - 1

x_m =0.075 - 1 = -0.925.

Wave pulse on a string shown in figure is moving to the right without changing shape. Consider two particles at positions x₁ = 1.5 m and x₂= 2.5 m. Their transverse velocities at the moment shown in figure are along directions

positive y-axis and positive y-axis respectively
negative y-axis and positive y-axis respectively
positive y-axis and negative y-axis respectively
negative y-axis and negative y-axis respectively

Solution

Dotted shape shows pulse position after a short time interval. Direction of the velocities are decided according to direction of displacements of the particles.

Let \(\overrightarrow{C}=\overrightarrow{A}+\overrightarrow{B}\)

\(\left |\overrightarrow{C} \right |\) is always greater than \(\left |\overrightarrow{A} \right |\)
It is possible to have \(\left |\overrightarrow{C} \right | < \left | \overrightarrow{A} \right | and \left |\overrightarrow{C} \right | < \left | \overrightarrow{B} \right |\)
\(\overrightarrow{C}\) is always equal to \(\overrightarrow{A}+\overrightarrow{B}\)
\(\overrightarrow{C}\) is never equal to \(\overrightarrow{A}+\overrightarrow{B}\)

A galvanometer of 50 ohm resistance has 25 divisions. A current of 4 × 10^–4 ampere gives a deflection of one division.To convert this galvanometer into a voltmeter having a range of 25 volts, it should be connected with a resistance of

2450 Ω in series.
2500 Ω in series.
245 Ω in series.
2550 Ω in series.

Solution

A bomb is released from a horizontal flying aeroplane. The trajectory of bomb is

a parabola
a straight line
a circle
a hyperbola

Solution

a parabola

Moment of inertia of a circular wire of mass M and radius R about its diameter is

MR²/2
MR²
2MR²
MR²/4

The instantaneous angular position of a point on a rotating wheel is given by the equation θ(t) = 2t³– 6t². The torque on the wheel becomes zero at

t = 1s
t= 0.5s
t= 0.25 s
t = 2s

Solution

Directions: Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer(ONLY ONE option is correct ) from the following.

Statement-1 :Adiabatic expansion is always accompanied by fall in temperature.

Statement-2 :In adiabatic process, volume is inversely proportional to temperature.

(a)Statement-1 is false, Statement-2 is true
(b)Statement-1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1
(c)Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1
(d)Statement-1 is true, Statement-2 is false

Solution

(d)Statement-1 is true, Statement-2 is false

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