JEE Main Physics — Mechanics previous year questions with solutions.
 In the diagram shown, the difference in the two tubes of the manometer is $5\mathrm{cm}$, the cross-section of the tube at $A$ and $B$ is $6{\mathrm{mm}}^{2}$ and $10{\mathrm{mm}}^{2}$ respectively. The rate at which water flows through the tube is $(g=10m{s}^{-2})$
When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude F = ax + bx$^{2}$ where a and b are constants. The work done in stretching the unstretched rubber-band by L is :
A large number of liquid drops each of radius $r$ coalesce to form a single drop of the radius $R$. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given surface tension of the liquid $T$, density $\rho$)
The average mass of rain drops is $3.0 \times 10^{-5} \mathrm{~kg}$ and their avarage terminal velocity is $9 \mathrm{~m} / \mathrm{s}$. Calculate the energy transferred by rain to each square metre of the surface at a place which receives $100 \mathrm{~cm}$ of rain in a year.
An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be :
A ball of mass $160g$ is thrown up at an angle of $60^{\circ}$ to the horizontal at a speed of $10m{s}^{-1}$. The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly $(g=10m{s}^{-2})$
A thin bar of length $\mathrm{L}$ has a mass per unit length $\lambda$, that increases linearly with distance from one end. If its total mass is $M$ and its mass per unit length at the lighter end is $\lambda_{\mathrm{O}}$, then the distance of the centre of mass from the lighter end is:
 A particle is released on a vertical smooth semicircular track from point $X$ so that, $OX$ makes angle $\theta$ from the vertical (see figure). The normal reaction of the track on the particle vanishes at the point $Y$ where $OY$ makes an angle $\phi$ with the horizontal. Then
A heavy box is to be dragged along a rough horizontal floor. To do so, the person $A$ pushes it at an angle $30^{\circ}$ from the horizontal and requires a minimum force ${F}_{A}$, while the person $B$ pulls the box at an angle $60^{\circ}$ from the horizontal and needs minimum force ${F}_{B}$. If the coefficient of friction between the box and the floor is $\frac{\sqrt{3}}{5}$, the ratio $\frac{{F}_{A}}{{F}_{B}}$ is
A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity $0.8$ ). The height of water is $3 \mathrm{~m}$ and that of kerosene $2 \mathrm{~m}$. When the hole is opened the velocity of fluid coming out from it is nearly: (take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ and density of water $\left.=10^3 \mathrm{~kg} \mathrm{~m}^{-3}\right)$
A capillary tube is immersed vertically in water and the height of the water column is $x$. When this arrangement is taken into a mine of depth d, the height of the water column is $y$. If R is the radius of earth, the ratio $\frac{ x }{ y }$ is :
Steel ruptures when a shear of $3.5 \times 10^8 \mathrm{~N} \mathrm{~m}^{-2}$ is applied. The force needed to punch a $1 \mathrm{~cm}$ diameter hole in a steel sheet $0.3 \mathrm{~cm}$ thick is nearly:
A bullet of mass $4 \mathrm{~g}$ is fired horizontally with a speed of $300 \mathrm{~m} / \mathrm{s}$ into $0.8 \mathrm{~kg}$ block of wood at rest on a table. If the coefficient of friction between the block and the table is $0.3$, how far will the block slide approximately?
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? 
Four particles, each of mass $M$ and equidistant from each other, move along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is
Two springs of force constants $300 \mathrm{~N} / \mathrm{m}$ (Spring A) and $400 \mathrm{~N} / \mathrm{m}$ (Spring B) are joined together in series. The combination is compressed by $8.75 \mathrm{~cm}$. The ratio of energy stored in $\mathrm{A}$ and $\mathrm{B}$ is $\frac{E_A}{E_B}$. Then $\frac{E_A}{E_B}$ is equal to:
A projectile of mass $M$ is fired so that the horizontal range is $4 \mathrm{~km}$. At the highest point the projectile explodes in two parts of masses $M / 4$ and $3 M / 4$ respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is :
A body starts from rest on a long inclined plane of slope $45^{\circ}$. The coefficient of friction between the body and the plane varies as $\mu=0.3 x$, where $x$ is distance travelled down the plane. The body will have maximum speed (for $g=10 \mathrm{~m} / \mathrm{s}^2$ ) when $x=$
A body of mass ' $m$ ' is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is $1 \mathrm{~cm}$. If the angular velocity is doubled, the elongation in the spring is $5 \mathrm{~cm}$. The original length of the spring is :
A tennis ball (treated as hollow spherical shell) starting from $\mathrm{O}$ rolls down a hill. At point $\mathrm{A}$ the ball becomes air borne leaving at an angle of $30^{\circ}$ with the horizontal. The ball strikes the ground at $\mathrm{B}$. What is the value of the distance $\mathrm{AB}$ ? (Moment of inertia of a spherical shell of mass $m$ and radius $R$ about its diameter $=\frac{2}{3} m R^2$ ) 
A particle of mass $2 \mathrm{~kg}$ is moving such that at time $t$, its position, in meter, is given by $\vec{r}(t)=5 \hat{i}-2 t^2 \hat{j}$. The angular momentum of the particle at $t=2 s$ about the origin in $\mathrm{kg} \mathrm{m}^{-2} \mathrm{~s}^{-1}$ is :
If the time period $t$ of the oscillation of a drop of liquid of density $d$, radius $r$, vibrating under surface tension $s$ is given by the formula $t=\sqrt{r^{2 b} s^c d^{a / 2}}$. It is observed that the time period is directly proportional to $\sqrt{\frac{d}{s}}$. The value of $b$ should therefore be :
In an experiment, a small steel ball falls through a liquid at a constant speed of $10 \mathrm{~cm} / \mathrm{s}$. If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward ?
Air of density $1.2 \mathrm{~kg} \mathrm{~m}^{-3}$ is blowing across the horizontal wings of an aeroplane in such a way that its speeds above and below the wings are $150 \mathrm{~ms}^{-1}$ and $100 \mathrm{~ms}^{-1}$, respectively. The pressure difference between the upper and lower sides of the wings, is :