JEE Main Physics — Mechanics previous year questions with solutions.
Match List - I with List - II. \(\begin{array}{llll} & \text{List - I} & & \text{List - II} \\ A. & \text{Coefficient of viscosity} & I. & [M L^{-1} T^{-1}] \\ B. & \text{Surface tension} & II. & [M L^{0} T^{-2}] \\ C. & \text{Pressure} & III. & [M L^{-1} T^{-2}] \\ D. & \text{Surface energy} & IV. & [M L^{2} T^{-2}] \end{array}\) Choose the correct answer from the options given below :
In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are $100$ divisions in circular scale and pitch of screw gauge is $0.1$ mm. When diameter of a sphere is measured, the reading of main scale is $5$ mm and $50^{\text{th}}$ division of circular scale coincides with the reference line of main scale. The diameter of sphere is _______ mm.
A new unit $(\alpha)$ of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of $\alpha$ units if light takes $6$ min. $40$ s to cover this distance?
A uniform solid cylinder of length $L$ and radius $R$ has moment of inertia about its axis equal to $I_{1}$. A small co-centric cylinder of length $L / 2$ and radius $R / 3$ carved from this cylinder has moment of inertia about its axis equals to $I_{2}$. The ratio $I_{1} / I_{2}$ is $\_\_\_\_$.
A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is $\_\_\_\_$ $\mathrm{kg}. \mathrm{m}^{2}$.
A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from its centre. The radius of gyration about this axis is $\sqrt{n} \mathrm{~cm}$. The value of $n$ is
Two cars $A$ and $B$ are moving in the same direction along a straight line with speeds $100$ km/h and $80$ km/h, respectively such that car $A$ is moving ahead of car $B$. A person in car $B$ throws a stone with a speed $v$ so that it hits the car $A$ with a speed of $5$ m/s. The value of $v$ is ______ km/h.
The potential energy of a particle changes with distance $x$ from a fixed origin as $V = \dfrac{A\sqrt{x}}{x + B}$, where $A$ and $B$ are constant with appropriate dimensions. The dimensions of $AB$ are _______.
A cube has side length $5$ cm and modulus of rigidity $10^5$ N/m$^2$. The displacement produced by a force of $10$ N in the upper face of cube is _____ mm.
In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division $=0.05 \mathrm{~mm}$, then the least count of the vernier callipers is $\_\_\_\_$ mm.
The position of center of mass of three masses $2$ kg, $3$ kg and $15$ kg placed with respect to mid point ($p$) of normal bisector, as shown in the figure is _______. 
A solid cylinder having radius $R$ and length $L$ is slipping on a rough horizontal plane. At time $t=0$ the cylinder has a translational velocity $v_0=49$ m/s, perpendicular to its axis and a rotational velocity $v_0/4R$ about the centre. The time taken by the cylinder to start rolling is ________ seconds. (coefficient of kinetic friction $\mu_K=0.25$ and $g=9.8$ m/s$^2$)
A block takes $t$ time to slide down a plane inclined at $45°$ to the horizontal. If the surface is made smooth (frictionless), the block takes time $\dfrac{t}{2}$ to slide down the plane. The coefficient of friction between the block and the inclined plane is $\left(\dfrac{\alpha}{100}\right)$. The value of $\alpha$ is __________.
The increase in the pressure required to decrease the volume $(\Delta V)$ of water is $6.3 \times 10^7$ N/m$^2$. The percentage decrease in the volume is _____. (Bulk modulus of water $= 2.1 \times 10^9$ N/m$^2$.)
Moment of inertia about an axis $AB$ for a rod of mass $40$ kg and length $3$ m is same as that of a solid sphere of mass of $10$ kg and radius $R$ about an axis parallel to $AB$ axis with separation of $3$ m as shown in figure below. The value of $R$ is given as $\sqrt{\dfrac{\alpha}{2}}$. The value of $\alpha$ is _______. 
Initially a satellite of 100 kg is in a circular orbit of radius $1.5 \mathrm{R}_{\mathrm{E}}$. This satellite can be moved to a circular orbit of radius $3 R_{E}$ by supplying $\alpha \times 10^{6} \mathrm{~J}$ of energy. The value of $\alpha$ is $\_\_\_\_$. (Take Radius of Earth $R_{E}=6 \times 10^{6} \mathrm{~m}$ and $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$)
A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with $3 \mathrm{~m} / \mathrm{s}^{2}$. At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is $5 \mathrm{~m} / \mathrm{s}$. The initial height of the airplane is $\_\_\_\_$ m. $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
A spring of force constant $15 \mathrm{~N} / \mathrm{m}$ is cut into two pieces. If the ratio of their length is $1: 3$, then the force constant of smaller piece is $\_\_\_\_$ $\mathrm{N} / \mathrm{m}$.
A particle of mass $m$ falls from rest through a resistive medium having resistive force, $F=-k v$, where $v$ is the velocity of the particle and $k$ is a constant. Which of the following graphs represents velocity ($v$) versus time ($t$)?
A string $A$ of length $0.314$ m and Young's modulus $2 \times 10^{10}$ N/m$^2$ is connected to another string $B$ of length and Young's modulus both twice of those of $A$. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass $0.8$ kg. The net change in length of the combination is _____ mm. (radius of both the strings is $0.2$ mm and acceleration due to gravity $= 10$ m/s$^2$) (Mass of both strings is to be neglected as compared to the mass of load)
A liquid of density $600$ kg/m$^3$ flowing steadily in a tube of varying cross-section. The cross-section at a point $A$ is $1.0$ cm$^2$ and that at $B$ is $20$ mm$^2$. Both the points $A$ and $B$ are in same horizontal plane, the speed of the liquid at $A$ is $10$ cm/s. The difference in pressures at $A$ and $B$ points is ________ Pa.
Consider a modified Bernoulli equation. $\left(\mathrm{P}+\frac{A}{B t^{2}}\right)+\rho g(h+B t)+\frac{1}{2} \rho V^{2}=$ constant If $t$ has the dimension of time then the dimensions of $A$ and $B$ are $\_\_\_\_$, $\_\_\_\_$ respectively.
Consider the equation $H = \dfrac{x^p \epsilon^q E^r}{t^s}$, where $H=$ magnetic field; $E=$ electric field, $\epsilon=$ permittivity, $x=$ distance, $t=$ time. The values of $p, q, r$ and $s$ respectively are:
In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg, moving in opposite directions with speeds of $10 \mathrm{~m} / \mathrm{s}$ and $30 \mathrm{~m} / \mathrm{s}$, respectively, strike each other and stick together. The rise in temperature (in ${ }^{\circ} \mathrm{C}$), if all the heat produced during the collision is retained by these spheres, is : (specific heat of sphere material $31 \mathrm{cal} / \mathrm{kg}.{ }^{\circ} \mathrm{C}$ and $1 \mathrm{cal}=4.2 \mathrm{~J}$)