JEE Main Physics — Mechanics previous year questions with solutions.
Assume that a drop of a liquid evaporates by a decrease in its surface energy so that its temperature remains unchanged. The minimum radius of the drop for this to be possible is. (The surface tension is $T$, the density of the liquid is$\rho$ and $L$ is its latent heat of vaporisation.)
A projectile is given an initial velocity of $(\hat{i}+2\hat{j})m{s}^{-1}$, where $\hat{\text{i}}$ is along the ground and $\hat{\text{j}}$ is along the vertical upward. If $g=10m{s}^{-2}$, the equation of its trajectory is :
The dimensions of angular momentum, latent heat and capacitance are, respectively.
The gravitational field, due to the 'left over part' of a uniform sphere (from which a part as shown, has been 'removed out'), at a very far off point, $\mathrm{P}$, located as shown, would be (nearly) : 
Wax is coated on the inner wall of a capillary tube and the tube is then dipped in water. Then, compared to the unwaxed capillary, the angle of contact $\theta$ and the height $h$ upto which water rises change. These changes are :
The distance travelled by a body moving along a line in time $t$ is proportional to $t^3$. The acceleration-time $(a, t)$ graph for the motion of the body will be
In a cylindrical water tank, there are two small holes $A$ and $B$ on the wall at a depth of $h_1$, from the surface of water and at a height of $h_2$ from the bottom of water tank. Surface of water is at height of $h_2$ from the bottom of water tank. Surface of water is at heigh $H$ from the bottom of water tank. Water coming out from both holes strikes the ground at the same point $S$. Find the ratio of $h_1$ and $h_2$ 
A block of weight $W$ rests on a horizontal floor with coefficient of static friction $\mu$. It is desired to make the block move by applying minimum amount of force. The angle $\theta$ from the horizontal at which the force should be applied and magnitude of the force $F$ are respectively.
$N$ divisions on the main scale of a vernier calliper coincide with $(N+1)$ divisions of the vernier scale. If each division of main scale is ' $a$ ' units, then the least count of the instrument is
The force $\vec{F}=F \hat{i}$ on a particle of mass $2 \mathrm{~kg}$, moving along the $x$-axis is given in the figure as a function of its position $x$. The particle is moving with a velocity of $5 \mathrm{~m} / \mathrm{s}$ along the $x$-axis at $x=0$. What is the kinetic energy of the particle at $x=8 \mathrm{~m} ?$ 
A particle gets displaced by $\Delta \bar{r}=(2 \hat{i}+3 \hat{j}+4 \hat{k}) \mathrm{m}$ under the action of a force $\vec{F}=(7 \hat{i}+4 \hat{j}+3 \hat{k})$. The change in its kinetic energy is
A particle of mass $\mathrm{m}$ is at rest at the origin at time $\mathrm{t}=0$. It is subjected to a force $\mathrm{F}(\mathrm{t})=\mathrm{F}_0 \mathrm{e}^{-\mathrm{bt}}$ in the $x$ direction. Its speed $v(t)$ is depicted by which of the following curves?
Two point masses of mass $m_1=f M$ and $m_2=(1-f) M(f < 1)$ are in outer space (far from gravitational influence of other objects) at a distance $R$ from each other. They move in circular orbits about their centre of mass with angular velocities $\omega_1$ for $m_1$ and $\omega_2$ for $m_2$. In that case
A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading: $58.5$ degree Vernier scale reading : $09$ divisions Given that $1$ division on main scale corresponds to $0.5$ degree. Total divisions on the vernier scale is $30$ and match with $29$ divisions of the main scale. The angle of the prism from the above data
A stone of mass $m$, tied to the end of a string, is whirled around in a circle on a horizontal frictionless table. The length of the string is reduced gradually keeping the angular momentum of the stone about the centre of the circle constant. Then, the tension in the string is given by $T=A r^n$, where $A$ is a constant, $r$ is the instantaneous radius of the circle. The value of $n$ is equal to
A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $1.5 \times 10^{-2} \mathrm{~N}$ (see figure). The length of the slider is $30 \mathrm{~cm}$ and its weight negligible. The surface tension of the liquid film is 
Two bodies $A$ and $B$ of mass $m$ and $2 m$ respectively are placed on a smooth floor. They are connected by a spring of negligible mass. $A$ third body $C$ of mass $m$ is placed on the floor. The body $C$ moves with a velocity $v_0$ along the line joining $A$ and $B$ and collides elastically with $A$. At a certain time after the collision it is found that the instantaneous velocities of $A$ and $B$ are same and the compression of the spring is $x_0$. The spring constant $k$ will be
A spring is compressed between two blocks of masses $m_1$ and $m_2$ placed on a horizontal frictionless surface as shown in the figure. When the blocks are released, they have initial velocity of $v_1$ and $v_2$ as shown. The blocks travel distances $x_1$ and $x_2$ respectively before coming to rest. The ratio $\left(\frac{x_1}{x_2}\right)$ is 
A solid sphere is rolling on a surface as shown in figure, with a translational velocity $v \mathrm{~m} \mathrm{~s}^{-1}$. If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is 
A ball is dropped vertically downwards from a height $h$ above the ground. It hits the ground inelastically and bounces up vertically. Neglecting subsequent motion and air resistance, which of the following graph represents variation between speed $(v)$ and height $(h)$ correctly?
A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side of track. Its engine passes the pole with velocity $u$ and the guard's room passes with velocity $v$. The middle wagon of the train passes the pole with a velocity.
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. Statement 1: When moment of inertia $I$ of a body rotating about an axis with angular speed $\omega$ increases, its angular momentum $L$ is unchanged but the kinetic energy $K$ increases if there is no torque applied on it. Statement 2: $L=I \omega$, kinetic energy of rotation $=\frac{1}{2} I \omega^2$
Which graph correctly presents the variation of acceleration due to gravity with the distance from the centre of the earth (radius of the earth $=R_E$ )?
The load versus elongation graphs for four wires of same length and made of the same material are shown in the figure. The thinnest wire is represented by the line 