The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas.
Question: The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat, extracted from the source in a single cycle is : $\mathrm{p}_{0} \mathrm{v}_{0}$$\left(\frac{13}{2}\right) \mathrm{p}_{0} \mathrm{v}_{0}$$\left(\frac{11}{2}\right) p_{0} v_{0}$$4 \mathrm{p}_{0} \mathrm{v}_{0}$Correct Option: , 2 Solution:...
Read More →If a source of power
Question: If a source of power $4 \mathrm{~kW}$ produces $10^{20}$ photons/second, the radiation belongs to apart of the spectrum called :-$\gamma$-raysX-raysultraviolet raysmicrowavesCorrect Option: , 2 Solution:...
Read More →In the circuit shown here, the point ' C ' is kept connected to point ' A '
Question: In the circuit shown here, the point ' $\mathrm{C}$ ' is kept connected to point ' $\mathrm{A}$ ' till the current flowing through the circuit becomes constant. Afterward, suddenly, point ' $C$ ' is disconnected from point ' $A$ ' and connected to point ' $B$ ' at time $t=0$. Ratio of the voltage across resistance and the inductor at $\mathrm{t}=\mathrm{L} /$ R will be equal to: $-1$$\frac{1-e}{e}$$\frac{e}{1-e}$1Correct Option: 1 Solution:...
Read More →A Carnot engine, whose efficiency is
Question: A Carnot engine, whose efficiency is $40 \%$ takes in heat from a source maintained at a temperature of $500 \mathrm{~K}$. It is desired to have an engine of efficiency $60 \%$. Then, the intake temperature for the same exhaust (sink) temperature must be :- $600 \mathrm{~K}$efficiency of Carnot engine cannot be made larger than $50 \%$$1200 \mathrm{~K}$$750 \mathrm{~K}$Correct Option: , 4 Solution:...
Read More →A particle of mass
Question: A particle of mass $m$ is moving along the side of a square of side ' $a$ ', with a uniform speed $v$ in the $x$-y plane as shown in the figure : Which of the following statement is false for the angular momentum $\overrightarrow{\mathrm{L}}$ about the origin ?$\overrightarrow{\mathrm{L}}=\frac{\mathrm{mv}}{\sqrt{2}} \mathrm{R} \hat{\mathrm{k}}$ when the particle is moving from $\mathrm{D}$ to $\mathrm{A}$$\overrightarrow{\mathrm{L}}=-\frac{\mathrm{mv}}{\sqrt{2}} \mathrm{R} \hat{\mathr...
Read More →A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm.
Question: A circular loop of radius $0.3 \mathrm{~cm}$ lies parallel to a much bigger circular loop of radius $20 \mathrm{~cm}$. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 $\mathrm{cm}$. If a current of $2.0$ A flows through the smaller loop, then the flux linked with bigger loop is :-$9.1 \times 10^{-11}$ weber$6 \times 10^{-11}$ weber$3.3 \times 10^{-11}$ weber$6.6 \times 10^{-9}$ weberCorrect Option: 1 Solution:...
Read More →Helium gas goes through a cycle
Question: Helium gas goes through a cycle $\mathrm{ABCDA}$ (consisting of two isochoric and two isobaric lines) as shown in figure. Efficiency of this cycle is nearly (Assume the gas to be close to ideal gas) :- $12.5 \%$$15.4 \%$$9.1 \%$$10.5 \%$Correct Option: , 2 Solution:...
Read More →From a solid sphere of mass
Question: From a solid sphere of mass $\mathrm{M}$ and radius $\mathrm{R}$ a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is:-$\frac{4 \mathrm{MR}^{2}}{9 \sqrt{3} \pi}$$\frac{4 \mathrm{MR}^{2}}{3 \sqrt{3} \pi}$$\frac{\mathrm{MR}^{2}}{32 \sqrt{2} \pi}$$\frac{\mathrm{MR}^{2}}{16 \sqrt{2} \pi}$Correct Option: 1 Solution:...
Read More →A metallic rod of length 'l' is tied to a string of length 21 and made to rotate with angular speed
Question: A metallic rod of length 'l' is tied to a string of length 21 and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field ' $\mathrm{B}$ ' in the region, the e.m.f. induced across the ends of the rod is : $\frac{2 \mathrm{B \omega} \mathrm{l}^{2}}{2}$$\frac{3 B \omega l^{2}}{2}$$\frac{4 \mathrm{~B} \omega \mathrm{l}^{2}}{2}$$\frac{5 \mathrm{~B} \omega \mathrm{l}^{2}}{2}$Correct Option: , 4 Solution:...
Read More →A radioactive nucleus A with a half life
Question: A radioactive nucleus $\mathrm{A}$ with a half life $\mathrm{T}$, decays into a nucleus $\mathrm{B}$. At $\mathrm{t}=0$, there is no nucleus B. At sometime $t$, the ratio of the number of $B$ to that of $A$ is $0.3$. Then, $t$ is given by :$\mathrm{t}=\mathrm{T} \log (1.3)$$t=\frac{T}{\log (1.3)}$$t=\frac{T}{2} \frac{\log 2}{\log 1.3}$$t=T \frac{\log 1.3}{\log 2}$Correct Option: , 4 Solution:...
Read More →A container with insulating walls is divided into two equal parts by a partition fitted with a valve.
Question: A container with insulating walls is divided into two equal parts by a partition fitted with a valve. One part is filled with an ideal gas at a pressure $P$ and temperature T, whereas the other part is completely evacuated. If the valve is suddenly opened, the pressure and temperature of the gas will be :- $\frac{\mathrm{P}}{2}, \mathrm{~T}$$\frac{\mathrm{P}}{2}, \frac{\mathrm{T}}{2}$$\mathrm{P}, \mathrm{T}$$\mathrm{P}, \frac{\mathrm{T}}{2}$Correct Option: 1 Solution:...
Read More →A mass ' m ' is supported
Question: A mass ' $m$ ' is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder, with what acceleration will the mass fall on release? $\frac{5 \mathrm{~g}}{6}$$\mathrm{g}$$\frac{2 g}{3}$$\frac{\mathrm{g}}{2}$Correct Option: , 4 Solution:...
Read More →A coil is suspended in a uniform magnetic field,
Question: 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 :- Electromagnetic induction in the aluminium plate giving rise to electromagnetic dampingDevelopment of air current when the plate is placedInduction of electrical charge on the plateShielding of ma...
Read More →Half-lives of two radioactive elements
Question: Half-lives of two radioactive elements $\mathrm{A}$ and $\mathrm{B}$ are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of $A$ and $B$ nuclei will be :-$5: 4$$1: 16$$4: 1$$1: 4$Correct Option: 1 Solution:...
Read More →A horizontal straight wire 20 m long extending from east to west is falling with a speed of
Question: A horizontal straight wire $20 \mathrm{~m}$ long extending from east to west is falling with a speed of $5.0 \mathrm{~m} / \mathrm{s}$, at right angles to the horizontal component of the earth's magnetic field $0.30 \times 10^{-4} \mathrm{~Wb} / \mathrm{m}^{2}$. The instantaneous value of the e.m.f. induced in the wire will be :-$6.0 \mathrm{mV}$$3 \mathrm{mV}$$4.5 \mathrm{mV}$$1.5 \mathrm{mV}$Correct Option: , 2 Solution:...
Read More →A bob of mass
Question: A bob of mass $\mathrm{m}$ attached to an inextensible string of length $\ell$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $\omega \mathrm{rad} / \mathrm{s}$ about the vertical. About the point of suspension :Angular momentum changes in direction but not in magnitudeAngular momentum changes both in direction and magnitudeAngular momentum is conservedAngular momentum changes in magnitude but not in direction.Correct Option: 1 Soluti...
Read More →The specific heat capacity of a metal at low temperautre
Question: The specific heat capacity of a metal at low temperautre $(T)$ is given as $C_{p}\left(k J J k^{-1} k g^{-1}\right)=32\left(\frac{T}{400}\right)^{3}$ A 100 gram vessel of this metal is to be cooled from $20^{\circ} \mathrm{K}$ to $4^{\circ} \mathrm{K}$ by a special refrigerator operating at room temperature $\left(27^{\circ} \mathrm{C}\right)$. The amount of work required to cool the vessel is:- equal to $0.002 \mathrm{~kJ}$greater than $0.148 \mathrm{~kJ}$between $0.148 \mathrm{~kJ}$ ...
Read More →A hoop of radius
Question: A hoop of radius $\mathrm{r}$ and mass $m$ rotating with an angular velocity $\omega_{0}$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip ?$\frac{r \omega_{0}}{4}$$\frac{r \omega_{0}}{3}$$\frac{\mathrm{r} \omega_{0}}{2}$$r \omega_{0}$Correct Option: , 3 Solution:...
Read More →A boat is moving due east in a region where the earth's magnetic field is
Question: A boat is moving due east in a region where the earth's magnetic field is $5.0 \times 10^{-5} \mathrm{NA}^{-1} \mathrm{~m}^{-1}$ due north and horizontal. The boat carries a vertical aerial $2 \mathrm{~m}$ long. If the speed of the boat is $1.50 \mathrm{~ms}^{-1}$, the magnitude of the indueced emf in the wire of aerial is :-$0.50 \mathrm{mV}$$0.15 \mathrm{mV}$$1 \mathrm{mV}$$0.75 \mathrm{mV}$Correct Option: , 2 Solution:...
Read More →The half life of a radioactive substance is 20 minutes.
Question: The half life of a radioactive substance is 20 minutes. The approximate time interval $\left(t_{2}-t_{1}\right)$ between the time $t_{2}$ when $\frac{2}{3}$ of it has decayed and time $t_{1}$ when $\frac{1}{3}$ of it had decayed is :-$20 \mathrm{~min}$$28 \mathrm{~min}$$7 \mathrm{~min}$$14 \mathrm{~min}$Correct Option: 1 Solution:...
Read More →A Carnot engine operating between temperatures
Question: A Carnot engine operating between temperatures $T_{1}$ and $T_{2}$ has efficientcy $\frac{1}{6}$. When $T_{2}$ is lowered by $62 \mathrm{~K}$, its efficiency increases to $\frac{1}{3}$. Then $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ are, respectively:- $330 \mathrm{~K}$ and $268 \mathrm{~K}$$310 \mathrm{~K}$ and $248 \mathrm{~K}$$372 \mathrm{~K}$ and $310 \mathrm{~K}$$372 \mathrm{~K}$ and $330 \mathrm{~K}$Correct Option: , 3 Solution:...
Read More →A particle of mass
Question: A particle of mass ' $m$ ' is projected with a velocity $\mathrm{v}$ making an angle of $30^{\circ}$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height ' $h$ ' is :-$\frac{\sqrt{3}}{2} \frac{\mathrm{mv}^{2}}{\mathrm{~g}}$zero$\frac{m v^{3}}{\sqrt{2} g}$$\frac{\sqrt{3}}{16} \frac{m v^{3}}{g}$Correct Option: , 4 Solution:...
Read More →A rectangular loop has a sliding connector PQ of length
Question: A rectangular loop has a sliding connector PQ of length $\ell$ and resistance $R \Omega$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $\mathrm{I}_{1}, \mathrm{I}_{2}$ and I are :- $\mathrm{I}_{1}=\mathrm{I}_{2}=\frac{\mathrm{B} \ell \mathrm{v}}{6 \mathrm{R}}, \mathrm{I}=\frac{\mathrm{B} \ell \mathrm{v}}{3 \mathrm{R}}$$\mathrm{I}_{1}=-\mathrm{I}_{2}=\frac{\mathrm{B} \ell \mathrm{v}}{\ma...
Read More →A thin horizontal circular disc
Question: A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc :-continuously increasesfirst increases and then decreasesremains unchangedcontinuously decresesCorrect Option: , 2 Solution:...
Read More →A diatomic ideal gas is used in a carnot engine as the working substance.
Question: A diatomic ideal gas is used in a carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from $\mathrm{V}$ to $32 \mathrm{~V}$, the efficiency of the engine is :- $0.25$$0.5$$0.75$$0.99$Correct Option: , 3 Solution:...
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