Question 1 :
On a $X$ temperature scale, water freezes at $-125.0^o$ X and boils at $375.0^o X$ . On a $Y$ temperature scale water freezes at $-70.0^o Y$ and boils at $-30.0^o Y $ . The value of temperature on $X$ scale equals to the temperature of $50.0^o Y $ on $Y-$ scale is :
Question 3 :
If the mass of a planet is $10\%$ less than that of the earth and the radius is $20\%$ greater than that of the earth, the acceleration due to gravity on the planet will be.
Question 4 :
A cavity of radius $R/2$ is made inside a solid sphere of radius $R$. The centre of the cavity is located at a distance $R/2$ from the centre of the sphere. The gravitational force on a particle of mass $m$ at a distance $R/2$ from the centre of the sphere on the line joining both the centres of the sphere and the cavity is (opposite to the centre of the cavity)<br>[Here $g=(GM)/{R}^{2}$, where $M$ is the mass of the sphere]<br>
Question 5 :
If $g_E$ and $g_M$ are the accelerations due to gravity on the surface of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio<br/><br/>$\displaystyle \frac {electronic\  charge\  on\  the\  moon}{electronic\  charge\  on\  the\  earth}$to be
Question 6 :
Assertion: If earth suddenly stops rotating about its axis, then the value of acceleration due to gravity will become same at all the places.
Reason: The value of acceleration due to gravity is independent of rotation of earth.
Question 7 :
Two balls are dropped from the same height from places $A$ and $B$. The body at $B$ takes two seconds less to reach the ground at $B$ strikes the ground with a velocity greater than at $A$ by $10 m/s$. The product of the acceleration due to gravity at the two places $A$ and $B$ is:
Question 8 :
A wooden cube is placed on a rough horizontal table, a force is applied to the cube. Gradually the force is increased.<br>Whether the cube slides before toppling or topples before sliding is independent of:<br>
Question 9 :
{tex} A {/tex} and {tex} B {/tex} are moving in 2 circular orbits with angular velocity {tex} 2 \omega {/tex} and {tex} \omega {/tex} respectively. Their positions are as shown at {tex} t = 0 . {/tex} Find the time when they will meet for the first time.<br>{tex} ( b ) {/tex}<br><img style='object-fit:contain' src="https://data-screenshots.sgp1.digitaloceanspaces.com/5e0f245b7ca27b1884a2d51c.jpg" />
Question 10 :
A hollow smooth uniform sphere {tex} A {/tex} of mass {tex} \mathrm { m } {/tex} rolls without sliding on a smooth horizontal surface. It collides head on elastically with another stationary smooth solid sphere {tex} B {/tex} of the same mass {tex} m {/tex} and same radius. The ratio of kinetic energy of {tex} B {/tex} to that of {tex} A {/tex} just after the collision is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5d5e844106864d5bec7be6f4">
Question 11 :
Two circular discs of same mass and thickness are made up of two different metals with densities {tex} d _ { X } {/tex} and {tex} d _ { Y } \left( d _ { X } > d _ { Y } \right) . {/tex} Their moments of inertia about the axes passing through their centers of gravity and perpendicular to their planes are {tex} I _ { X } {/tex} and {tex} I _ { Y } {/tex}. Which one is correct?
Question 12 :
The moment of inertia of a uniform circular disc of radius 'R' and mass 'M' about an axis passing from the edge of the disc and normal to the disc is
Question 13 :
A particle of mass {tex} m {/tex} is attached to a thin uniform rod of length a and mass {tex} 4 \mathrm { m } {/tex}. The distance of the particle from the centre of mass of the rod is {tex} a / 4 {/tex}. The moment of inertia of the combination about an axis passing through O normal to the rod is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e0f0fa14faa335027dc77fd"><br>
Question 14 :
A wheel having moment of inertia {tex} 2 \mathrm { kg } - \mathrm { m } ^ { 2 } {/tex} about its vertical axis, rotates at the rate of {tex} 60 \mathrm { rpm } {/tex} about this axis, The torque which can stop the wheel's rotation in one minute would be
Question 15 :
If {tex} \overrightarrow { \mathrm { F } } {/tex} is the force acting on a particle having position vector {tex} \overrightarrow { \mathrm { r } } {/tex} and {tex} \vec { \tau } {/tex} be the torque of this force about the origin, then:
Question 16 :
A thin wire of length {tex} L {/tex} and uniform linear mass density {tex} \rho {/tex} is bent into a<br>circular loop with centre at {tex} O {/tex} as shown. The moment of inertia of the loop about the axis {tex} X X {/tex} is<br> <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/NEET/5e0f2fb04faa335027dc7911' />
Question 17 :
The moment of inertia of a hollow thick spherical shell of mass Mand its inner radius {tex} \mathrm { R } _ { 1 } {/tex} and outer radius {tex} \mathrm { R } _ { 2 } {/tex} about its diameter is
Question 18 :
The moment of inertia of a uniform semicircular wire of mass {tex} \mathrm { m } {/tex} and radius {tex} \mathrm { r } , {/tex} about an axis passing through its centre of mass and perpendicular to its plane is {tex} \mathrm { mr } ^ { 2 } \left( 1 - \frac { \mathrm { k } } { \pi ^ { 2 } } \right) . {/tex} Find the value of {tex} \mathrm { k } {/tex} .<br>
Question 19 :
Two bodies have their moments of inertia {tex} \small \mathrm I {/tex} and {tex} \small \mathrm {2I} {/tex} respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio
Question 20 :
Two rods of different materials having coefficients of thermal expansion and Young's moduli ${Y}_{1}, {Y}_{2}$, respectively are fixed between two rigid massive walls. The rods are heated such that undergo the same increase in temperature. There is no bending of the rods. If ${\alpha}_{1}:{\alpha}_{2}= 2:3$, the thermal stresses developed in the two rods are equal provided ${Y}_{1}: {Y}_{2}$ is equal to:<br/>
Question 21 :
Two persons pull a rope towards themselves. Each person exerts a force of {tex} 100 \mathrm { N } {/tex} on the rope. Find the Young's modulus of the material of the rope if it extends in length by {tex} 1 \mathrm { cm } {/tex}. Original length of the rope {tex} = 2 \mathrm { m } {/tex} and the area of cross-section {tex} = 2 \mathrm { cm } ^ { 2 } . {/tex}
Question 22 :
The ratio of the lengths of two rods is $4:3 $ . The ratio of their coefficients of cubical expasion is $ 2:3 $ . Then the ratio of their liner expansions when they are heated through same temperature difference is :
Question 23 :
A rubber ball is brought into 200 m deep water, its volume is decreased by 0.1% then volume  elasticity coefficient of the material of ball will be:<br/>$(Given\ \rho = 10^3 kg/m^3$ and $ g = 9.8 ms^{-2})$
Question 24 :
A black body has maximum wavelength {tex} \lambda _ { m } {/tex} at temperature 2000{tex} \mathrm { K } {/tex} . Its corresponding wavelength at temperature 3000 {tex} \mathrm { K } {/tex} will be
Question 25 :
The specific heat capacity of a metal at low temperature (T) is given as {tex} C _ { p } \left( k J K ^ { - 1 } \mathrm { kg } ^ { - 1 } \right) = 32 \left( \frac { T } { 400 } \right) ^ { 3 } {/tex}. A {tex}100{/tex} gram vessel of this metal is to be cooled from {tex} 20 ^ { \circ } \mathrm { K } {/tex} to {tex} 4 ^ { \circ } \mathrm { K } {/tex} by a special refrigerator operating at room temperature {tex} \left( 27 ^ { \circ } \mathrm { C } \right) . {/tex} The amount of work required to cool the vessel is
Question 26 :
Which of the following statements is/are false about mode of heat transfer?
Question 27 :
The radiation energy density per unit wavelength at a temperature {tex}\mathrm T{/tex} has a maximum at a wavelength {tex} \lambda _ { 0 } . {/tex} At temperature {tex} 2 \mathrm { T } , {/tex} it will have a maximum wavelength
Question 28 :
Two wires of different material and radius have their length in ratio of $1:2.$ if these were stretched by the same force$,$ the strain produced will be in the ratio$.$  
Question 29 :
A piece of ice falls from a height h so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h is: {tex} \left. \text { [Latent heat of ice is } 3.4 \times 10 ^ { 5 } \mathrm { J } / \mathrm { kg } = 10 \mathrm { N } / \mathrm { kg } \right] {/tex}<br>
Question 30 :
A graph is plotted with PV/T on y-axis and mass of the gas along {tex} x {/tex} -axis for different gases. The graph is
Question 31 :
One kg of a diatomic gas is at a pressure of {tex} 8 \times 10 ^ { 4 } \mathrm { N } / \mathrm { m } ^ { 2 } . {/tex} Th density of the gas is {tex} 4 \mathrm { kg } / \mathrm { m } ^ { 3 } . {/tex} What is the energy of the ga due to its thermal motion?
Question 32 :
Consider a gas with density {tex} \rho {/tex} and {tex} \overline { c } {/tex} as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity {tex} v , {/tex} then the pressure exerted by the gas is
Question 33 :
A vessel has 6{tex} \mathrm { g } {/tex} of hydrogen at pressure {tex} \mathrm { P } {/tex} and temperature 500{tex} \mathrm { K } {/tex} . A small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure is {tex} \mathrm { P } / 2 {/tex} and temperature falls to 300{tex} \mathrm { K } ? {/tex}
Question 34 :
If the potential energy of a gas molecule is {tex} \mathrm { U } = \mathrm { M } / \mathrm { r } ^ { 6 } - \mathrm { N } / \mathrm { r } ^ { 12 } , \mathrm { M } {/tex} and {tex} \mathrm { N } {/tex} being positive constants. Then the potential energy at equilibrium must be
Question 35 :
At {tex} 10 ^ { \circ } \mathrm { C } {/tex} the value of the density of a fixed mass of an ideal gas divided by its pressure is {tex} {x } {/tex} . At {tex} 110 ^ { \circ } \mathrm { C } {/tex} this ratio is:
Question 36 :
1 mole of a monatomic and 2 mole of a diatomic gas are mixed. The resulting gas is taken through a process in which molar heat capacity was found 3{tex} \mathrm { R } {/tex} . Polytropic constant in the process is
Question 37 :
The absolute temperature of a gas is increases 3 times. The root mean square velocity of the molecules increases
Question 38 :
How is the mean free path {tex} ( \lambda ) {/tex} in a gas related to the interatomic distance?
Question 39 :
A gas mixture consists of 2 moles of oxygen and 4 moles of Argon at temperature T. Neglecting all vibrational moles, the total internal energy of the system is
Question 40 :
Find the size of object which can be featured with $5\space MHz$ in water.
Question 41 :
The frequency of fork is 512 Hz and the sound produced by it travels 42 metres as the tuning fork completes 64 vibrations. Find the velocity of sound :<br/>
Question 42 :
The frequency of a man's voice is 300 Hz and its wavelength is 1 meter. If the wavelength of a child's voice is 1.5 m, then the frequency of the child's voice is :<br>
Question 43 :
Equations of a stationary wave and a travelling wave are ${ y }_{ 1 } = a\ sinkx\ cos \omega t$ and ${ y }_{ 2 } = a\ sin (\omega t - kx)$. The phase difference between two points ${ x }_{ 1 }\ =\ \dfrac { \pi }{ 3k } \ and\ { x }_{ 2 }\ =\ \dfrac { 3\pi }{ 2k } \ is\ { \phi }_{ 1 }$ for the first wave and ${ \phi }_{ 2 }$ for the second wave. The ratio $\dfrac { { \phi }_{ 1 } }{ { \phi }_{ 2 } }$ is :
Question 44 :
Two identical piano wires kept under the same tension T have a fundamental frequency of 600{tex} \mathrm { Hz } {/tex} . The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beats/s when both the wires oscillate together would be
Question 45 :
A wave of frequency 500 Hz has a phase velocity of 360 m/s. The phase difference between the two displacements at a certain point in a time interval of 10$^{-3}$ seconds will be how much?