JEE Main Physics — Mechanics previous year questions with solutions.
A car is moving with speed of $150\mathrm{km}{h}^{-1}$ and after applying the brake it will move $27m$ before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling _____ $m$ distance.
Four spheres each of mass $m$ form $a$ square of side $d$ (as shown in figure). A fifth sphere of mass $M$ is situated at the centre of square. The total gravitational potential energy of the system is 
A stone tide to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is $\sqrt{x({u}^{2}-gL)}$. The value of $x$ is
The variation of acceleration due to gravity $(g)$ with distance $(r)$ from the center of the earth is correctly represented by (Given $R=$ radius of earth)
The one division of main scale of vernier callipers reads $1\mathrm{mm}$ and $10$ divisions of Vernier scale is equal to the $9$ divisions on main scale. When the two jaws of the instrument touch each other the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between $4.1\mathrm{cm}$ and $4.2\mathrm{cm}$ and ${6}^{\mathrm{th}}$ Vernier division coincides with a main scale division. The diameter of the bob will be _____ ${10}^{-2}\mathrm{cm}$.
A student in the laboratory measures thickness of a wire using screw gauge. The readings are $1.22\mathrm{mm},1.23\mathrm{mm},1.19\mathrm{mm}$ and $1.20\mathrm{mm}$. The percentage error is $\frac{x}{121}%$. The value of $x$ is _____ .
Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block in the direction of the lighter block. The velocity of the center of mass is:
A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration ${a}_{c}$ is varying with time $t$ as ${a}_{c}={k}^{2}r{t}^{2}$ , where $k$ is a constant. The power delivered to the particle by the force acting on it is -
The velocity of upper layer of water in a river is $36\mathrm{km}{h}^{-1}$. Shearing stress between horizontal layers of water is ${10}^{-3}N{m}^{-2}$. Depth of the river is _____ $m$. (Co-efficient of viscosity of water is ${10}^{-2}\mathrm{Pa}s$)
A block of mass $10\mathrm{kg}$ starts sliding on a surface with an initial velocity of $9.8{\mathrm{ms}}^{-1}$. The coefficient of friction between the surface and block is $0.5$. The distance covered by the block before coming to rest is :[use $g=9.8{\mathrm{ms}}^{-2}$]
A man of $60\mathrm{kg}$ is running on the road and suddenly jumps into a stationary trolly car of mass $120\mathrm{kg}$. Then the trolly car starts moving with velocity $2{ms}^{-1}$. The velocity of the running man was _____ $m{s}^{-1}$, when he jumps into the car.
A uniform heavy rod of mass $20\mathrm{kg}$. Cross sectional area $0.4{m}^{2}$ and length $20m$ is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is $x\times {10}^{-9}m$. The value of $x$ is _____ . (Given. Young's modulus $Y=2\times {10}^{11}{\mathrm{Nm}}^{-2}$ and $g=10m{s}^{-2}$ )
A particle experiences a variable force $\vec{F}=(4x\hat{i}+3{y}^{2}\hat{j})$ in a horizontal $x-y$ plane. Assume distance in meters and force is newton. If the particle moves from point $(1,2)$ to point $(2,3)$ in the $x-y$ plane, then Kinetic Energy changes by :
The percentage decrease in the weight of a rocket, when taken to a height of $32\mathrm{km}$ above the surface of earth will, be (Radius of earth $=6400\mathrm{km}$)
A system of two blocks of masses $m=2\mathrm{kg}$ and $M=8\mathrm{kg}$ is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is $0.5$. The maximum horizontal force $F$ that can be applied to the block of mass $M$ so that the blocks move together will be $(g=9.8m{s}^{-2})$ 
One end of a massless spring of spring constant $k$ and natural length ${l}_{0}$ is fixed while the other end is connected to a small object of mass $m$ lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity $\omega$ about an axis passing trough fixed end, then the elongation of the spring will be
The velocity of a small ball of mass $0.3g$ and density $8g{\mathrm{cc}}^{-1}$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $1.3g{\mathrm{cc}}^{-1}$, then the value of viscous force acting on the ball will be $x\times {10}^{-4}N$, the value of $x$ is _____ . [use $g=10m{s}^{-2}$]
An object of mass $1\mathrm{kg}$ is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, $g=10m{s}^{-2}$ and radius of earth $=6400\mathrm{km}$]
A $0.5\mathrm{kg}$ block moving at a speed of $12{\mathrm{ms}}^{-1}$ compresses a spring through a distance $30\mathrm{cm}$ when its speed is halved. The spring constant of the spring will be _____ ${\mathrm{Nm}}^{-1}$
A thin circular ring of mass $M$ and radius $R$ is rotating with a constant angular velocity $2\mathrm{rad}{s}^{-1}$ in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass $m$ be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in $\mathrm{rad}{s}^{-1}$).
Sand is being dropped from a stationary dropper at a rate of $0.5\mathrm{kg}{s}^{-1}$ on a conveyor belt moving with a velocity of $5m{s}^{-1}$. The power needed to keep belt moving with the same velocity will be
A mass of $10\mathrm{kg}$ is suspended vertically by a rope of length $5m$ from the roof. A force of $30N$ is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is $\alpha ={\mathrm{tan}}^{-1}(x\times {10}^{-1})$. The value of $x$ is _____ . (Given, $g=10m{s}^{-2}$)
If $\vec{A}=(2\hat{i}+3\hat{j}-\hat{k})m$ and $\vec{B}=(\hat{i}+2\hat{j}+2\hat{k})m$. The magnitude of component of vector $\vec{A}$ along vector $\vec{B}$ will be _____ $m$.
In an experiment of determine the Young's modulus of wire of a length exactly $1m$, the extension in the length of the wire is measured as $0.4\mathrm{mm}$ with an uncertainty of $\pm 0.02\mathrm{mm}$ when a load of $1\mathrm{kg}$ is applied. The diameter of the wire is measured as $0.4\mathrm{mm}$ with an uncertainty of $\pm 0.01\mathrm{mm}$. The error in the measurement of Young's modulus $(\Delta Y)$ is found to be $x\times {10}^{10}N{m}^{-2}$. The value of $x$ is _____ .