JEE Main Physics — Mechanics previous year questions with solutions.
A ball having kinetic energy KE, is projected at an angle of $60^{\circ}$ from the horizontal. What will be the kinetic energy of ball at the highest point of its flight ?
The range of a projectile launched with initial velocity u at angle θ with horizontal is given by:
The displacement x versus time graph is shown below.  (A) The average velocity during 0 to 3 s is $10 \mathrm{~m} / \mathrm{s}$ (B) The average velocity during 3 to 5 s is $0 \mathrm{~m} / \mathrm{s}$ (C) The instantaneous velocity at $\mathrm{t}=2 \mathrm{~s}$ is $5 \mathrm{~m} / \mathrm{s}$ (D) The average velocity during 5 to 7 s and instantaneous velocity at $\mathrm{t}=6.5 \mathrm{~s}$ are equal (E) The average velocity from $t=0$ to $t=9 \mathrm{~s}$ is zero Choose the correct answer from the options given below:
A force $\mathrm{f}=\mathrm{x}^2 \mathrm{y} \hat{\mathrm{i}}+\mathrm{y}^2 \hat{\mathrm{j}}$ acts on a particle in a plane $\mathrm{x}+\mathrm{y}=10$. The work done by this force during a displacement from $(0,0)$ to $(4 \mathrm{~m}, 2 \mathrm{~m})$ is $\qquad$ Joule (round off to the nearest integer)
The maximum speed of a boat in still water is \(27 \mathrm{~km} / \mathrm{h}\). Now this boat is moving downstream in a river flowing at \(9 \mathrm{~km} / \mathrm{h}\). A man in the boat throws a ball vertically upwards with speed of \(10 \mathrm{~m} / \mathrm{s}\). Range of the ball as observed by an observer at rest on the river bank, is _______ cm. (Take \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\))
A massless spring gets elongated by amount $x_1$ under a tension of 5 N . Its elongation is $x_2$ under the tension of 7 N . For the elongation of $\left(5 x_1-2 x_2\right)$, the tension in the spring will be,
The energy of a system is given as $\mathrm{E}(\mathrm{t})=\alpha^3 \mathrm{e}^{-\beta t}$, where t is the time and $\beta=0.3 \mathrm{~s}^{-1}$. The errors in the measurement of $\alpha$ and $t$ are $1.2 \%$ and $1.6 \%$, respectively. At $t=5 \mathrm{~s}$, maximum percentage error in the energy is :
Two cars $P$ and $Q$ are moving on a road in the same direction. Acceleration of car $P$ increases linearly with time whereas car $Q$ moves with a constant acceleration. Both cars cross each other at time $t=0$, for the first time. The maximum possible number of crossing(s) (including the crossing at $t=0)$ is ________.
A particle is projected with velocity $u$ so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as $\frac{n u^2}{25 g}$, where value of $n$ is : (Given ' $g$ ' is the acceleration due to gravity).
An object of mass 1000 g experiences a time dependent force $\vec{F}=\left(2 t \hat{i}+3 t^2 \hat{j}\right) N$. The power generated by the force at time $t$ is :
A body of mass $m$ is suspended by two strings making angles $\theta_1$ and $\theta_2$ with the horizontal ceiling with tensions $T_1$ and $T_2$ simultaneously. $T_1$ and $T_2$ are related by $T_1=\sqrt{3} T_2$. the angles $\theta_1$ and $\theta_2$ are
In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $\mathrm{M}^{\mathrm{P}} \mathrm{L}^{\mathrm{Q}} \mathrm{T}^{\mathrm{R}} \mathrm{A}^{\mathrm{S}}$, where value of ' Q ' and ' R ' are
Match the LIST-I withLIST-II Choose the correct answer from the options given below :
Moment of inertia of a rod of mass ' M ' and length 'L' about an axis passing through its center and normal to its length is ' $\alpha$ '. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cross about an axis passing through its center and normal to plane containing cross is :
 Three equal masses $m$ are kept at vertices (A, B, C) of an equilateral triangle of side a in free space. At $t=0$, they are given an initial velocity $\vec{V}_A=V_0 \overrightarrow{A C}, \vec{V}_B=V_0 \overrightarrow{B A}$ and $\vec{V}_C=V_0 \overrightarrow{C B}$. Here, $\overrightarrow{A C}, \overrightarrow{C B}$ and $\overrightarrow{B A}$ are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is :
A rod of length 5 L is bent right angle keeping one side length as 2 L.  The position of the centre of mass of the system: (Consider $\mathrm{L}=10 \mathrm{~cm}$)
A square Lamina OABC of length 10 cm is pivoted at 'O'. Forces act at Lamina as shown in figure. If Lamina remains stationary, then the magnitude of F is : 
The electric flux is $\phi=\alpha \sigma+\beta \lambda$ where $\lambda$ and $\sigma$ are linear and surface charge density, respectively. $\left(\frac{\alpha}{\beta}\right)$ represents
The least count of a screw guage is 0.01 mm . If the pitch is increased by $75 \%$ and number of divisions on the circular scale is reduced by $50 \%$, the new least count will be _____ $\times 10^{-3} \mathrm{~mm}$
If $\overrightarrow{\mathrm{L}}$ and $\overrightarrow{\mathrm{P}}$ represent the angular momentum and linear momentum respectively of a particle of mass ' m ' having position vector $\overrightarrow{\mathrm{r}}=\mathrm{a}(\hat{\mathrm{i}} \cos \omega \mathrm{t}+\hat{\mathrm{j}} \sin \omega \mathrm{t})$. The direction of force is
In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of $\left[M^P L^{\circ} \mathrm{T}^{\mathrm{R}} \mathrm{A}^{\mathrm{S}}\right]$. The value of P and Q are :
 A string of length $L$ is fixed at one end and carries a mass of $M$ at the other end. The mass makes $\left(\frac{3}{\pi}\right)$ rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is $\ldots\ldots$ ML.
Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is ______ .
The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between $t=0$ to $t=4 \mathrm{~s}$ ? 