JEE Main Physics — Mechanics previous year questions with solutions.
A bob of mass $m$ is suspended at a point $O$ by a light string of length $l$ and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity $v_0$ at the point ' A ', the string becomes slack when, the bob reaches at the point ' D '. The ratio of the kinetic energy of the bob at the points $B$ and $C$ is ______ -. 
Given below are two statements: Statement I: The hot water flows faster than cold water Statement II: Soap water has higher surface tension as compared to fresh water. In the light above statements, choose the correct answer from the options given below
Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is $P_1$. The reading of the pressure gauge falls to $P_2$ when the valve is opened. The speed of water flowing in the pipe is proportional to
The coordinates of a particle with respect to origin in a given reference frame is \((1,1,1)\) meters. If a force of \(\overrightarrow{\mathrm{F}}=\hat{i}-\hat{j}+\hat{k}\) acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is ______.
A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)
A particle moves along the $x$-axis and has its displacement $x$ varying with time $t$ according to the equation $\mathrm{x}=\mathrm{c}_0\left(\mathrm{t}^2-2\right)+\mathrm{c}(\mathrm{t}-2)^2$ where $c_0$ and $c$ are constants of appropriate dimensions. Then, which of the following statements is correct?
An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density $1000 \mathrm{~kg} / \mathrm{m}^3$. If the pressure inside the bubble is $2100 \mathrm{~N} / \mathrm{m}^2$ greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )
A force $\mathrm{F}=\alpha+\beta \mathrm{x}^2$ acts on an object in the x -direction. The work done by the force is 5 J when the object is displaced by 1 m . If the constant $\alpha=1 \mathrm{~N}$ then $\beta$ will be
 A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :
A solid circular disc of mass $50\mathrm{kg}$ rolls along a horizontal floor so that its center of mass has a speed of $0.4m{s}^{-1}$. The absolute value of work done on the disc to stop it is ______ $J$.
The density and breaking stress of a wire are $6 \times 10^4 \mathrm{~kg} / \mathrm{m}^3$ and $1.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1}{3}^{\text {rd }}$ of the value on the surface of earth. The maximum length of the wire with breaking is _____ m (take, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ).
Two persons pull a wire towards themselves. Each person exerts a force of $200 \mathrm{~N}$ on the wire. Young's modulus of the material of wire is $1 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$. Original length of the wire is $2 \mathrm{~m}$ and the area of cross section is $2 \mathrm{~cm}^2$. The wire will extend in length by ______ $\mu \mathrm{m}$.
If average depth of an ocean is $4000m$ and the bulk modulus of water is $2\times {10}^{9}N{m}^{-2}$, then fractional compression $\frac{\Delta V}{V}$ of water at the bottom of ocean is $\alpha \times {10}^{-2}$. The value of $\alpha$ is _______, (Given, $g=10m{s}^{-2},\rho =1000\mathrm{kg}{m}^{-3}$)
The resistance $R=\frac{V}{I}$, where $V=(200\pm 5)V$ and $I=(20\pm 0.2)A$, the percentage error in the measurement of $R$ is :
A liquid column of height $0.04 \mathrm{~cm}$ balances excess pressure of a soap bubble of certain radius. If density of liquid is $8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$ and surface tension of soap solution is $0.28 \mathrm{Nm}^{-1}$, then diameter of the soap bubble is _____ $\mathrm{cm}$. (if $g=10 \mathrm{~m} \mathrm{~s}^{-2}$ )
A small ball of mass $m$ and density $\rho$ is dropped in a viscous liquid of density $\rho_0$. After sometime, the ball falls with constant velocity. The viscous force on the ball is :
A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is $\frac{10}{x}$. The value of $x$ is __________
A small spherical ball of radius $r$, falling through a viscous medium of negligible density has terminal velocity $v$. Another ball of the same mass but of radius $2r$, falling through the same viscous medium will have terminal velocity:
Given below are two statements: Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $P_1-P_2=\rho g\left(h_2-h_1\right)$. Statement II : In ventury tube shown $2 \mathrm{gh}=v_1^2-v_2^2$  In the light of the above statements, choose the most appropriate answer from the options given below.
A small liquid drop of radius $R$ is divided into $27$ identical liquid drops. If the surface tension is $T$, then the work done in the process will be :
A physical quantity $Q$ is found to depend on quantities $a,b,c$ by the relation $Q=\frac{{a}^{4}{b}^{3}}{{c}^{2}}$. The percentage error in $a,b$ and $c$ are $3%,4%$ and $5%$ respectively. Then, the percentage error in $Q$ is:
In an experiment to measure focal length $(f)$ of convex lens, the least counts of the measuring scales for the position of object $(\mathrm{u})$ and for the position of image $(\mathrm{v})$ are $\Delta \mathrm{u}$ and $\Delta \mathrm{v}$, respectively. The error in the measurement of the focal length of the convex lens will be:
$10$ divisions on the main scale of a Vernier calliper coincide with $11$ divisions on the Vernier scale. If each division on the main scale is of $5$ units, the least count of the instrument is :
A soap bubble is blown to a diameter of $7 \mathrm{~cm} .36960 \mathrm{erg}$ of work is done in blowing it further. If surface tension of soap solution is $40 \mathrm{dyne} / \mathrm{cm}$ then the new radius is______ $\mathrm{cm}$ Take $\left(\pi=\frac{22}{7}\right)$