Question 1 :
Two balls are projected simultaneously in the same vertical plane from the same point with velocities {tex} v _ { 1 } {/tex} and {tex} v _ { 2 } {/tex} with angle {tex} \theta _ { 1 } {/tex} and {tex} \theta _ { 2 } {/tex} respectively with the horizontal. If {tex} v _ { 1 } {/tex} cos {tex} \theta _ { 1 } = v _ { 2 } \cos \theta _ { 2 } , {/tex} the path of one ball as seen from the position of other ball is:
Question 2 :
A bullet is fired with a speed of {tex} 1500 \mathrm { m } / \mathrm { s } {/tex} in order to hit a target {tex} 100 \mathrm { m } {/tex} away. If {tex} \mathrm { g } = 10 \mathrm { m } / \mathrm { s } ^ { 2 } . {/tex} The gun should be aimed
Question 3 :
A solid sphere, a hollow sphere and a solid cylinder, all having equal mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are equal and but not sufficient to allow pure rolling. Greastest time will be taken in reaching the bottom by
Question 4 :
If {tex} n {/tex} bullets each of mass {tex} m {/tex} are fired with a velocity {tex} v {/tex} per second from a machine gun, the force required to hold the gun in position is
Question 5 :
The minimum force required to start pushing a body up rough (frictional coefficient {tex} \mu ) {/tex} inclined plane is {tex} F _ { 1 } {/tex} while the minimum force needed to prevent it from sliding down is {tex} F _ { 2 } {/tex}. If the inclined plane makes an angle {tex} \theta {/tex} from the horizontal such that {tex} \tan \theta = 2 \mu {/tex} then the ratio {tex} \frac { F _ { 1 } } { F _ { 2 } } {/tex} is
Question 6 :
A particle of mass {tex} m {/tex} rotates with a uniform angular speed {tex} \omega . {/tex} It is viewed from a frame rotating about the Z-axis with a uniform angular velocity {tex} \omega _ { 0 } . {/tex} The centrifugal force on the particle is:
Question 7 :
The coefficient of restitution e for a perfectly elastic collision is
Question 8 :
In an inelastic collision, which of the following does not remain conserved?
Question 9 :
A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table?
Question 10 :
A force of $5N$ is applied on a $20kg$ mass at rest. The work done in the third second is,
Question 11 : From a circular disc of radius {tex} R {/tex} and mass {tex} 9 M , {/tex} a small disc of radius {tex} R / 3 {/tex} is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to th plane of the disc and passing through {tex} O {/tex} is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e0f0faf4faa335027dc7808">
Question 12 : A tangential force of {tex} 20 \mathrm { N } {/tex} is applied on a cylinder of mass {tex} 4 \mathrm { kg } {/tex} and moment of inertia {tex} 0.02 \mathrm { kg } \mathrm { m } ^ { 2 } {/tex} about its own axis. If the cylinder rolls without slipping, then linear acceleration of its centre of mass will be<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e0f0fbb4faa335027dc7812">
Question 13 : {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 14 :
A circular disc of radius {tex} R {/tex} is removed from a bigger circular disc of radius {tex} 2 \mathrm { R } {/tex} such that the circumferences of the discs coincide. The centre of mass of the new disc is {tex} \alpha / \mathrm { R } {/tex} form the centre of the bigger disc. The value of {tex} \alpha {/tex} is
Question 15 :
On a new scale of temperature (which is linear) and called the W scale, the freezing and boiling points of water are 39°W and 239°W respectively. What will be the temperature on the new scale, corresponding to a temperature of 39°C on the Celsius scale ?
Question 16 :
On a hypothetical scale A the ice point is $42^o$ and the steam point is $182^o$ For another scale B, the ice point is $-10^o$ and steam point in $90^o$) If B reads $60^o$, the reading of A is,
Question 17 :
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 18 :
Air is pumped into an automobile tube upto a pressure of 200{tex} \mathrm { kPa } {/tex} in the morning when the air temperature is {tex} 22 ^ { \circ } \mathrm { C } {/tex} . During the day, temperature rises to {tex} 42 ^ { \circ } \mathrm { C } {/tex} and the tube expands by 2{tex} \% {/tex} . The pressure of the air in the tube at this temperature, will be approximately
Question 19 :
The density of a gas is {tex} 6 \times 10 ^ { - 2 } \mathrm { kg } / \mathrm { m } ^ { 3 } {/tex} and the root mean square velocity of the gas molecules is 500{tex} \mathrm { m } / \mathrm { s } {/tex} . The pressure exerted by the gas on the walls of the vessel is
Question 20 :
N molecules, each of mass <b>m</b> of gas <b>A</b> and <b>2N</b> molecules, each of mass <b>2m</b>, of gas <b>B</b> are contained in the same vessel which is maintained at a temperature <b>T</b>. The mean square velocity of molecules of <b>B</b> type is denoted by <b>V<sub>2</sub></b> and the mean square velocity of <b>A</b> type is denoted by <b>V<sub>1</sub></b> then {tex} \frac { \mathrm { V } _ { 1 } } { \mathrm { V } _ { 2 } } {/tex} is
Question 21 :
For a gas, if ratio of specific heats at constant pressure and volume is {tex} \gamma {/tex} then value of degrees of freedom is
Question 22 :
A spherical planet, far out in space, has a mass $M_0$ and diameter $D_0$. A particle of mass $m$ falling freely near the surface of this planet will experience acceleration due to gravity which is equal to:
Question 23 :
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 24 :
Two spheres of different materials one with double the radius and one-fourth wall thickness of the other are filled with ice. If the time taken for complete melting of ice in the larger sphere is 25 minute and for smaller one is 16 minute, the ratio of thermal conductivities of the materials of larger spheres to that of smaller sphere is<br>
Question 25 :
In a Young's double slit experiment, the intensity at the cetral maximum is $l_{0-}$. The intensity ata distance $\beta/4$ from the central maximum is ($\beta $is frige width)
Question 26 :
The density of water at {tex} 20 ^ { \circ } \mathrm { C } {/tex} is 998{tex} \mathrm { kg } / \mathrm { m } ^ { 3 } {/tex} and at {tex} 40 ^ { \circ } \mathrm { C } \ 992 {/tex} {tex} \mathrm { kg } / \mathrm { m } ^ { 3 } . {/tex} The coefficient of volume expansion of water is
Question 27 :
A travelling wave is represented by the equation $y=20 sin (20 \pi t - 5x)$. The angular frequency of the wave is
Question 28 :
A sinusoidal progressive wave is generated in a string. It's equation is given by $y=(2 mm)   \sin (2\pi x - 100\pi t + \pi/3).$ The time when particle at $x = 4 m$ first passes through mean position, will be 
Question 29 :
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 30 :
The equation of a progressive wave are $Y=\sin{\left[200\pi\left(t-\cfrac{x}{330}\right)\right]}$, where $x$ is in meter and f is second. The frequency and velocity of wave are
