JEE Main Physics — Mechanics previous year questions with solutions.
Two liquids A and B have $\theta_{\mathrm{A}}$ and $\theta_{\mathrm{B}}$ as contact angles in a capillary tube. If $K=\cos \theta_A / \cos \theta_B$. then identify the correct statement:
For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equals to 15 cm. The vernier scale attached to the microscope has 25 divisions equals to 24 divisions of main scale. The least count (LC) of the travelling microscope is (in cm) :
The pair of physical quantities not having same dimensions is :
Match List-I with List-II. $\begin{array}{|l|l|l|l|} \hline & \text{List-I} & & \text{List-II} \\ \hline \text{(A)} & \text{Mass density} & \text{(I)} & {\left[\mathrm{ML}^2 \mathrm{~T}^{-3}\right]} \\ \hline \text{(B)} & \text{Impulse} & \text{(II)} & {\left[\mathrm{MLT}^{-1}\right]} \\ \hline \text{(C)} & \text{Power} & \text{(III)} & {\left[\mathrm{ML}^2 \mathrm{~T}^0\right]} \\ \hline \text{(D)} & \text{Moment of inertia} & \text{(IV)} & {\left[\mathrm{ML}^{-3} \mathrm{~T}^0\right]} \\ \hline\end{array}$ Choose the correct answer from the options given below :
If $\epsilon_0$ denotes the permittivity of free space and $\Phi_{\mathrm{E}}$ is the flux of the electric field through the area bounded by the closed surface, then dimension of $\left(\epsilon_0 \frac{\mathrm{~d} \phi_{\mathrm{E}}}{\mathrm{dt}}\right)$ are that of :
The equation for real gas is given by $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where $\mathrm{P}, \mathrm{V}, \mathrm{T}$ and R are the pressure, volume, temperature and gas constant, respectively. The dimension of $\mathrm{ab}^{-2}$ is equivalent to that of :
An object of mass ' m ' is projected from origin in a vertical $x y$ plane at an angle $45^{\circ}$ with the x axis with an initial velocity $\mathrm{v}_0$. The magnitude and direction of the angular momentum of the object with respect to origin, when it reaches at the maximum height, will be [ g is acceleration due to gravity]
 A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitude of tensions $T_1$ and $T_2$, respectively, are (in N) :
A car of mass ' $m$ ' moves on a banked road having radius ' $r$ ' and banking angle $\theta$. To avoid slipping from banked road, the maximum permissible speed of the car is $v_0$. The coefficient of friction $\mu$ between the wheels of the car and the banked road is
The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of $7 \times 10^6 \mathrm{~Pa}$, would be ____ $\mathrm{mm}^3$. (Given bulk modulus of copper $=1.4 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$ )
A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is :
Two iron solid discs of negligible thickness have radii $R_1$ and $R_2$ and moment of intertia $I_1$ and $I_2$, respectively. For $R_2=2 R_1$, the ratio of $I_1$ and $I_2$ would be $1 / x$, where $\mathrm{x}=$ ________ -
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) :  Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities $v_{\mathrm{A}}=5 \mathrm{~m} / \mathrm{s}, v_{\mathrm{B}}=2 \mathrm{~m} / \mathrm{s}, v_{\mathrm{C}}=4 \mathrm{~m} / \mathrm{s}$. If we wait sufficiently long for elastic collision to happen, then $v_{\mathrm{A}}=4 \mathrm{~m} / \mathrm{s}, v_{\mathrm{B}}=2 \mathrm{~m} / \mathrm{s}$, $v_{\mathrm{C}}=5 \mathrm{~m} / \mathrm{s}$ will be the final velocities. Reason (R): In an elastic collision between identical masses, two objects exchange their velocities. In the light of the above statements, choose the correct answer from the options given below :
Match List - I with List - II. $$ \begin{array}{llll} & \text { List - I } & & \text { List - II } \\ \text { (A) } & \text { Permeability of free space } & \text { (I) }\left[\mathrm{M} \mathrm{~L}^2 \mathrm{~T}^{-2}\right] \\ \text { (B) } & \text { Magnetic field } & \text { (II) }\left[\mathrm{M} \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right] \\ \text { (C) } & \text { Magnetic moment } & \text { (III) }\left[\mathrm{M} \mathrm{~L} \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right] \\ \text { (D) } & \text { Torsional constant } & \text { (IV) }\left[\mathrm{L}^2 \mathrm{~A}\right] \end{array} $$ Choose the correct answer from the options given below :
Match List-I with List-II. $\begin{array}{ll} \text{List-I} & \text{List-II} \\ \text{(A) Coefficient of viscosity} & \text{(I) } \left[\mathrm{ML}^0 \mathrm{~T}^{-3}\right] \\ \text{(B) Intensity of wave} & \text{(II) } \left[\mathrm{ML}^{-2} \mathrm{~T}^{-2}\right] \\ \text{(C) Pressure gradient} & \text{(III) } \left[\mathrm{M}^{-1} \mathrm{LT}^2\right] \\ \text{(D) Compressibility} & \text{(IV) } \left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]\end{array}$ Choose the correct answer from the options given below :
Which one of the following forces cannot be expressed in terms of potential energy?
A block of mass 25 kg is pulled along a horizontal surface by a force at an angle $45^{\circ}$ with the horizontal. The friction coefficient between the block and the surface is 0.25. The displacement of 5 m of the block is:
A sand dropper drops sand of mass $m(t)$ on a conveyer belt at a rate proportional to the square root of speed $(v)$ of the belt, i.e. $\frac{\mathrm{dm}}{\mathrm{dt}} \propto \sqrt{v}$. If P is the power delivered to run the belt at constant speed then which of the following relationship is true?
Which one of the following is the correct dimensional formula for the capacitance in F ? $\mathrm{M}, \mathrm{L}, \mathrm{T}$ and C stand for unit of mass, length, time and charge,
A balloon and its content having mass $M$ is moving up with an acceleration ' $a$ '. The mass that must be released from the content so that the balloon starts moving up with an acceleration ' $3 a^{\prime}$ will be (Take ' g ' as acceleration due to gravity)
The center of mass of a thin rectangular plate (fig - x ) with sides of length $a$ and $b$, whose mass per unit area $(\sigma)$ varies as $\sigma=\frac{\sigma_0 x}{a b}$ (where $\sigma_0$ is a constant), would be $\qquad$ 
M and R be the mass and radius of a disc. A small disc of radius $R / 3$ is removed from the bigger disc as shown in figure. The moment of inertia of remaining part of bigger disc about an axis AB passing through the centre O and perpendicular to the plane of disc is $\frac{4}{x} M R^2$. The value of $x$ is ________. 
A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is $\sqrt{\frac{x}{5}}$ where $\mathrm{x}=$ _____
A solid sphere with uniform density and radius R is rotating initially with constant angular velocity $\left(\omega_1\right)$ about its diameter. After some time during the rotation its starts loosing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius become $R / 2$ is $x \omega_1$. The value of $x$ is ________