JEE Main Physics — Mechanics previous year questions with solutions.
The minimum and maximum distances of a planet revolving around the Sun are ${x}_{1}$ and ${x}_{2}$. If the minimum speed of the planet on its trajectory is ${v}_{0}$, then its maximum speed will be:
In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are $50$ divisions on the circular scale, and the main scale moves by $0.5\mathrm{mm}$ on a complete rotation. For a particular observation the reading on the main scale is $5\mathrm{mm}$ and the ${20}^{\text{th }}$ division of the circular scale coincides with reference line. Calculate the true reading.
The pitch of the screw gauge is $1\mathrm{mm}$ and there are $100$ divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies $8$ divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while ${72}^{\text{nd }}$ division on circular scale coincides with the reference line. The radius of the wire is
Consider a uniform wire of mass $M$ and length $L$. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is :
Water drops are falling from a nozzle of a shower onto the floor from a height of $9.8m$. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor.
The normal density of a material is $\rho$ and its bulk modulus of elasticity is $K$. The magnitude of increase in density of material, when a pressure $P$ is applied uniformly on all sides, will be :
The force is given in terms of time $t$ and displacement $x$ by the equation $F=A\mathrm{cos}Bx+C\mathrm{sin}Dt$ The dimensional formula of $\frac{AD}{B}$ is:
A player kicks a football with an initial speed of $25{ms}^{-1}$ at an angle of $45^{\circ}$ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion? (Take $g=10{ms}^{-2}$)
A body weighs $49N$ on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator? [Use $g=\frac{GM}{{R}^{2}}=9.8m{s}^{-2}$ and radius of earth, $R=6400\mathrm{km}.$]
A solid cylinder of mass $m$ is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is:  [The coefficient of static friction, ${\mu }_{s}$, is $0.4$ ]
A bullet of $10g$, moving with velocity $v$, collides head-on with the stationary bob of a pendulum and recoils with velocity $100m{s}^{-1}$. The length of the pendulum is $0.5m$ and mass of the bob is $1\mathrm{kg}$. The minimum value of $v\text{in}m{s}^{-1}$, so that the pendulum describes a circle. (Assume the string to be inextensible and $g=10m{s}^{-2}$ ) 
A force $\vec{F}=4\hat{i}+3\hat{j}+4\hat{k}$ is applied on an intersection point of $x=2$ plane and $x$-axis. The magnitude of torque of this force about a point $(2,3,4)$ is ________. (Round off to the Nearest Integer)
The average translational kinetic energy of ${N}_{2}$ gas molecules at $_________C\circ$ becomes equal to the $K.E.$ of an electron accelerated from rest through a potential difference of $0.1\mathrm{volt}.$ (Given ${k}_{B}=1.38\times {10}^{-23}J{K}^{-1})$ (Fill the nearest integer).
A car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ to come to rest. If the total time elapsed is t seconds, the total distance travelled is:
A geostationary satellite is orbiting around an arbitrary planet $P$ at a height of $11R$ above the surface of $P$, $R$ being the radius of $P$. The time period of another satellite in hours at a height of $2R$ from the surface of $P$ is ________ has the time period of $24\mathrm{hours}.$
The projectile motion of a particle of mass $5g$ is shown in the figure.  The initial velocity of the particle is $5\sqrt{2}{\mathrm{ms}}^{-1}$ and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points $A$ and $B$ is $x\times {10}^{-2}{\mathrm{kgms}}^{-1}$. The value of $x$, to the nearest integer, is ___ .
An engine of a train, moving with uniform acceleration, passes the signal-post with velocity $u$ and the last compartment with velocity $v$. The velocity with which middle point of the train passes the signal post is :
If two similar springs each of spring constant ${K}_{1}$ are joined in series, the new spring constant and time period would be changed by a factor:
$\mathrm{Assertion}A:$ If in five complete rotations of the circular scale, the distance travelled on the main scale of the screw gauge is $5\mathrm{mm}$ and there are $50$ total divisions on a circular scale, then the least count is $0.001\mathrm{cm}.$ $\mathrm{Reason}R:$ Least Count $=\frac{\text{ Pitch }}{\text{ Total divisions on circular scale }}$ In the light of the above statements, choose the most appropriate answer from the options given below.
Consider a binary star system of star $A$ and star $B$ with masses ${m}_{A}$ and ${m}_{B}$ revolving in a circular orbit of radii ${r}_{A}$ and ${r}_{B},$ respectively. If ${T}_{A}$ and ${T}_{B}$ are the time period of star $A$ and star $B,$ respectively, then:
Given below is the plot of a potential energy function $U(x)$ for a system, in which a particle is in one dimensional motion, while a conservative force $F(x)$ acts on it. Suppose that ${E}_{\text{mech }}=8J$, the incorrect statement for this system is : 
The centre of a wheel rolling on a plane surface moves with a speed ${v}_{0}.$ A particle on the rim of the wheel at the same level as the centre will be moving at a speed $\sqrt{x}{v}_{0}.$ Then the value of $x$ is $.$
A ball of mass $10\mathrm{kg}$ moving with a velocity $10\sqrt{3}m{s}^{-1}$ along the $x$ -axis, hits another ball of mass $20\mathrm{kg}$ which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along $y$ -axis with a speed of $10m{s}^{-1}.$ The second piece starts moving at an angle of $30^{\circ}$ with respect to the $x$ -axis. The velocity of the ball moving at $30^{\circ}$ with $x$ -axis is $xm{s}^{-1}.$ The configuration of pieces after the collision is shown in the figure below. The value of $x$ to the nearest integer is 
The resultant of these forces $\vec{OP},\vec{OQ},\vec{OR},\vec{OS}$ and $\vec{OT}$ is approximately ______$N.$<br>[Take $\sqrt{3}=1.7,\sqrt{2}=1.4$ Given $\hat{i}$ and $\hat{j}$ unit vectors along $x,y$ axis]<br><img src="https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/615f0e999476412f48314daf/Physics/images/Mathematics_in_Physics/648b5a6b417cc3fb48d67529/question_1__q_648b5a6b417cc3fb48d67529__cdn-question-pool.getmarks.app__7f3ed2a8-48d6-47b2-87ba-1dfc91732126-image__0e34012255_final_ppt_sync.png" alt="JEE Main 2021 Physics, Mathematics in Physics — question figure">