JEE Main Physics — Mechanics previous year questions with solutions.
The graph of an object's motion (along the $x-$ axis) is shown in the figure. The instantaneous velocity of the object at points $A$ and $B$ are $v_A$ and $v_B$ respectively. Then 
An engine pumps water continuously through a hose. Water leaves the hose with velocity $v$ and $m$ is mass per unit length of the water jet. If this jet hits a surface and came to rest instantaneously, the force on the surface is
A satellite moving with velocity $v$ in a force free space collects stationary interplanetary dust at a rate of $\frac{d M}{d t}=\alpha v$ where $M$ is the mass (of satellite + dust) at that instant. The instantaneous acceleration of the satellite is
A structural steel rod has a radius of $10 \mathrm{~mm}$ and length of $1.0 \mathrm{~m}$. A $100 \mathrm{kN}$ force stretches it along its length. Young's modulus of structural steel is $2 \times 10^{11} \mathrm{Nm}^{-2}$. The percentage strain is about
A moving particle of mass $m$, makes a head on elastic collision with another particle of mass $2 m$, which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to
Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are $3 \%$ each, then error in the value of resistance of the wire is
A square hole of side length $\ell$ is made at a depth of $\mathrm{h}$ and a circular hole of radius $\mathrm{r}$ is made at a depth of $4 \mathrm{~h}$ from the surface of water in a water tank kept on a horizontal surface. If $\ell< < h, r< < h$ and the rate of water flow from the holes is the same, then $r$ is equal to
A large number of droplets, each of radius, $r$ coalesce to form a bigger drop of radius, $R$. An engineer designs a machine so that the energy released in this process is converted into the kinetic energy of the drop. Velocity of the drop is ( $T=$ surface tension, $\rho=$ density)
A steel wire can sustain $100 \mathrm{~kg}$ weight without breaking. If the wire is cut into two equal parts, each part can sustain a weight of
Sand is being dropped on a conveyer belt at the rate of $2 \mathrm{~kg}$ per second. The force necessary to keep the belt moving with a constant speed of $3 \mathrm{~ms}^{-1}$ will be
A student measured the diameter of a wire using a screw gauge with the least count $0.001 \mathrm{~cm}$ and listed the measurements. The measured value should be recorded as
A solid sphere having mass $m$ and radius $r$ rolls down an inclined plane. Then its kinetic energy is
The amount of heat produced in an electric circuit depends upon the current $(I)$, resistance $(R)$ and time $(t)$. If the error made in the measurements of the above quantities are $2 \%, 1 \%$ and $1 \%$ respectively then the maximum possible error in the total heat produced will be
A car of mass $1000 \mathrm{~kg}$ is moving at a speed of 30 $\mathrm{m} / \mathrm{s}$. Brakes are applied to bring the car to rest. If the net retarding force is $5000 \mathrm{~N}$, the car comes to stop after travelling $d \mathrm{~m}$ in $t \mathrm{~s}$. Then
A boy can throw a stone up to a maximum height of $10 \mathrm{~m}$. The maximum horizontal distance that the boy can throw the same stone up to will be
A point particle is held on the axis of a ring of mass $m$ and radius $r$ at a distance $r$ from its centre $C$. When released, it reaches $C$ under the gravitational attraction of the ring. Its speed at $C$ will be
The electrical resistance $R$ of a conductor of length $l$ and area of cross section $a$ is given by $R=\frac{\rho l}{a}$ where ' $\rho$ ' is the electrical resistivity. What is the dimensional formula for electrical conductivity ' $\sigma$ ' which is reciprocal of resistivity?
This question has statement $1$ and statement $2$. Of the four choices given after the statements, choose the one that best describes the two statements. If two springs $\mathrm{S_1}$ and $\mathrm{S_2}$ of force constants $k_1$ and $k_2$, respectively, are stretched by the same force, it is found that more work is done on spring $\mathrm{S_1}$ than on spring $\mathrm{S_2}$. Statement $1$ : If stretched by the same amount, work done on $\mathrm{S}_1$, will be more than that on $\mathrm{S}_2$ Statement $2: k_1 < k_2$
Given that $K=$ energy, $V=$ velocity, $T=$ time. If they are chosen as the fundamental units, then what is dimensional formula for surface tension?
The terminal velocity of a small sphere of radius $a$ in a viscous liquid is proportional to
A projectile moving vertically upwards with a velocity of $200 \mathrm{~ms}^{-1}$ breaks into two equal parts at a height of $490 \mathrm{~m}$. One part starts moving vertically upwards with a velocity of $400 \mathrm{~ms}^{-1}$. How much time it will take, after the break up with the other part to hit the ground?
A circular hole of diameter $\mathrm{R}$ is cut from a disc of mass $M$ and radius $R$; the circumference of the cut passes through the centre of the disc. The moment of inertia of the remaining portion of the disc about an axis perpendicular to the disc and passing through its centre is
The mass of a spaceship is $1000 \mathrm{~kg}$. It is to be launched from the earth's surface out into free space. The value of ' $\mathrm{g}$ ' and ' $R$ ' (radius of earth) are $10 \mathrm{~m} / \mathrm{s}^2$ and $6400 \mathrm{~km}$ respectively. The required energy for this work will be ;
Water is flowing through a horizontal tube having cross-sectional areas of its two ends being $A$ and $A^{\prime}$ such that the ratio $A / A^{\prime}$ is 5 . If the pressure difference of water between the two ends is $3 \times$ $10^5 \mathrm{~N} \mathrm{~m}^{-2}$, the velocity of water with which it enters the tube will be (neglect gravity effects)