JEE Main Physics — Mechanics previous year questions with solutions.
Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude. Reason R: At equator, the direction of acceleration due to the gravity is towards the center of earth. In the light of above statements, choose the correct answer from the options given below
Two bodies of mass $1\mathrm{kg}$ and $3\mathrm{kg}$ have position vectors $\hat{i}+2\hat{j}+\hat{k}$ and $-3\hat{i}-2\hat{j}+\hat{k}$ respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :
A projectile is launched at an angle $\alpha$ with the horizontal with a velocity $20{ms}^{-1}$. After $10s$, its inclination with horizontal is $\beta$. The value of $\mathrm{tan}\beta$ will be : $(g=10{ms}^{-2})$.
A liquid of density $750\mathrm{kg}{m}^{-3}$ flows smoothly through a horizontal pipe that tapers in cross-sectional area from ${A}_{1}=1.2\times {10}^{-2}{m}^{2}$ to ${A}_{2}=\frac{{A}_{1}}{2}$. The pressure difference between the wide and narrow sections of the pipe is $4500\mathrm{Pa}$. The rate of flow of liquid is _____ $\times {10}^{-3}{m}^{3}{s}^{-1}$.
Three identical spheres each of mass $M$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $3m$ each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be $\sqrt{x}m$. The value of $x$ is
A uniform metal chain of mass $m$ and length $L$ passes over a massless and frictionless pulley. It is released from rest with a part of its length $l$ is hanging on one side and rest of its length $L-l$ is hanging on the other side of the pulley. At a certain point of time, when $l=\frac{L}{x}$, the acceleration of the chain is $\frac{g}{2}$. The value of $x$ is _____. 
A bag of sand of mass $9.8\mathrm{kg}$ is suspended by a rope. $A$ bullet of $200g$ travelling with speed $10{\mathrm{ms}}^{-1}$ gets embedded in it, then loss of kinetic energy will be
A tube of length $50\mathrm{cm}$ is filled completely with an incompressible liquid of mass $250g$ and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity $x\sqrt{F}\mathrm{rad}{s}^{-1}$. If $F$ be the force exerted by the liquid at the other end then the value of $x$ will be _____ .
The area of cross-section of a large tank is $0.5{m}^{2}$. It has a narrow opening near the bottom having area of cross-section $1{\mathrm{cm}}^{2}$. A load of $25\mathrm{kg}$ is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is $40\mathrm{cm}$ above the bottom, will be _____ $\mathrm{cm}{s}^{-1}$. [Take $g=10{ms}^{-2}$ ]
A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in $1\mathrm{cm}$ on main scale and $50$ Vernier scale divisions are equal to $49$ main scale divisions, then least count of the travelling microscope is _____ $\times {10}^{-6}m$.
A ball is thrown vertically upwards with a velocity of $19.6m{s}^{-1}$ from the top of a tower. The ball strikes the ground after $6s$. The height from the ground up to which the ball can rise will be $(\frac{k}{5})m$. The value of $k$ is _____ (use $g=9.8m{s}^{-2}$)
A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height $h$. Find the ratio of the times in which it is at height $\frac{h}{3}$ while going up and coming down respectively.
If momentum of a body is increased by $20%$, then its kinetic energy increases by :
If the acceleration due to gravity experienced by a point mass at a height $h$ above the surface of earth is same as that of the acceleration due to gravity at a depth $\alpha h(h\ll {R}_{e})$ ) from the earth surface. The value of $\alpha$ will be _____ . (use ${R}_{e}=6400\mathrm{km}$)
The bulk modulus of a liquid is $3\times {10}^{10}{\mathrm{Nm}}^{-2}$. The pressure required to reduce the volume of liquid by $2%$ is :
A spherical soap bubble of radius $3\mathrm{cm}$ is formed inside another spherical soap bubble of radius $6\mathrm{cm}$. If the internal pressure of the smaller bubble of radius $3\mathrm{cm}$ in the above system is equal to the internal pressure of the another single soap bubble of radius $r\mathrm{cm}$. The value of $r$ is _____
A bag is gently dropped on a conveyor belt moving at a speed of $2m{s}^{-1}$. The coefficient of friction between the conveyor belt and bag is $0.4$ Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion is : [Take $g=10m{s}^{-2}$]
A curved in a level road has a radius $75m$. The maximum speed of a car turning this curved road can be $30m{s}^{-1}$ without skidding. If radius of curved road is changed to $48m$ and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be _____ $m{s}^{-1}$.
A person moved from $A$ to $B$ on a circular path as shown in figure. If the distance travelled by him is $60m$, then the magnitude of displacement would be : (Given $\mathrm{cos}135^{\circ}=-0.7$)<br><img src="https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/615f0e999476412f48314daf/Physics/images/Mathematics_in_Physics/648b5a6c417cc3fb48d677e9/question_1__q_648b5a6c417cc3fb48d677e9__cdn-question-pool.getmarks.app__63bb7d82cb755babaefa1a6c__b623b2a5de_final_ppt_sync.jpg" alt="JEE Main 2022 Physics, Mathematics in Physics — question figure">
Consider the efficiency of Carnot's engine is given by $\eta =\frac{\alpha \beta }{\mathrm{sin}\theta }{\mathrm{log}}_{e}\frac{\beta x}{kT}$, where $\alpha$ and $\beta$ are constants. If $T$ is temperature, $k$ is Boltzman constant, $\theta$ is angular displacement and $x$ has the dimensions of length. Then, choose the incorrect option.
Two planets $A$ and $B$ of equal mass are having their period of revolutions ${T}_{A}$ and ${T}_{B}$ such that ${T}_{A}=2{T}_{B}$. These planets are revolving in the circular orbits of radii ${r}_{A}$ and ${r}_{B}$ respectively. Which out of the following would be the correct relationship of their orbits?
Moment of Inertia (M.I.) of four bodies having same mass $M$ and radius $2R$ are as follows ${I}_{1}=$ M.I. of solid sphere about its diameter ${I}_{2}=$ M.I. of solid cylinder about its axis ${I}_{3}=$ M.I. of solid circular disc about its diameter ${I}_{4}=$ M.I. of thin circular ring about its diameter If $2({I}_{2}+{I}_{3})+{I}_{4}=x{I}_{1}$ then the value of $x$ will be _____ .
Statement I : The law of gravitation holds good for any pair of bodies in the universe. Statement II : The weight of any person becomes zero when the person is at the centre of the earth. In the light of the above statements, choose the correct answer from the options given below.
A bullet of mass $200g$ having initial kinetic energy $90J$ is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to $40J$ within $1s$, the minimum length of the pool, the bullet has to travel so that it completely comes to rest is 