JEE Main Physics — Mechanics previous year questions with solutions.
A river is flowing from west to east direction with speed of $9 \mathrm{~km} \mathrm{~h}^{-1}$. If a boat capable of moving at a maximum speed of $27 \mathrm{~km} \mathrm{~h}^{-1}$ in still water, crosses the river in half a minute, while moving with maximum speed at an angle of $150^{\circ}$ to direction of river flow, then the width of the river is :
Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is $11.2 \mathrm{~km} / \mathrm{s}$, the escape velocity in $\mathrm{km} / \mathrm{s}$ from the planet will be :
The angle of projection of a particle is measured from the vertical axis as $\phi$ and the maximum height reached by the particle is $h_m$. Here $h_m$ as function of $\phi$ can be presented as
The expression given below shows the variation of velocity \((v)\) with time (t), \(v=\mathrm{At}^2+\frac{\mathrm{Bt}}{\mathrm{C}+\mathrm{t}}\). The dimension of ABC is :
Given below are two statements : Statement (I) : The dimensions of Planck's constant and angular momentum are same. Statement (II) : In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant. In the light of the above statements, choose the most appropriate answer from the options given below :
The position vector of a moving body at any instant of time is given as $\vec{r}=\left(5 t^2 \hat{i}-5 t \hat{j}\right) \mathrm{m}$. The magnitude and direction of velocity at $t=2 \mathrm{~s}$ is,
A particle is projected at an angle of $30^{\circ}$ from horizontal at a speed of $60 \mathrm{~m} / \mathrm{s}$. The height traversed by the particle in the first second is $\mathrm{h}_0$ and height traversed in the last second, before it reaches the maximum height, is $h_1$. The ratio $h_0: h_1$ is _________ [Take, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ]
Given a charge $q$, current I and permeability of vacuum $\mu_0$. Which of the following quantity has the dimension of momentum?
Two wires A and B are made of same material having ratio of lengths $\frac{L_A}{L_B}=\frac{1}{3}$ and their diameters ratio $\frac{d_A}{d_B}=2$. If both the wires are stretched using same force, what would be the ratio of their respective elongations?
A physical quantity C is related to four other quantities $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s as follows $\mathrm{C}=\frac{\mathrm{pq}^2}{\mathrm{r}^3 \sqrt{\mathrm{~s}}}$<br>The percentage errors in the measurement of $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s are $1 \%, 2 \% 3 \%$ and $2 \%$ respectively.<br>The percentage error in the measurement of C will be _____$\%$.
The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N , the length of the string is 1.56 m. The original length of the string is _____ m.
A solid steel ball of diameter 3.6 mm acquired terminal velocity $2.45 \times 10^{-2} \mathrm{~m} / \mathrm{s}$ while falling under gravity through an oil of density $925 \mathrm{~kg} \mathrm{~m}^{-3}$. Take density of steel as $7825 \mathrm{~kg} \mathrm{~m}^{-3}$ and g as 9.8 $\mathrm{m} / \mathrm{s}^2$. The viscosity of the oil in SI unit is
 Consider two blocks A and B of masses $m_1=10 \mathrm{~kg}$ and $m_2=5 \mathrm{~kg}$ that are placed on a frictionless table. The block A moves with a constant speed $v=3 \mathrm{~m} / \mathrm{s}$ towards the block B kept at rest. A spring with spring constant $\mathrm{k}=3000 \mathrm{~N} / \mathrm{m}$ is attached with the block B as shown in the figure. After the collision, suppose that the blocks A and B, along with the spring in constant compression state, move together, then the compression in the spring is, (Neglect the mass of the spring)
A rod of linear mass density ' $\lambda$ ' and length ' $L$ ' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameter is :
Two projectiles are fired from ground with same initial speeds from same point at angles $\left(45^{\circ}+\alpha\right)$ and $\left(45^{\circ}-\alpha\right)$ with horizontal direction. The ratio of their times of flights is
Which of the following curves possibly represent one-dimensional motion of a particle?     Choose the correct answer from the options given below :
A particle is released from height $S$ above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.
A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is $200 \mathrm{~N} / \mathrm{m}$. The block is pushed such that the length of the spring becomes 1 m and then released. At distance $\mathrm{x} \mathrm{m}(\mathrm{x} \lt 2)$ from the wall. the speed of the block will be :
In the experiment for measurement of viscosity ' $\eta$ ' of given liquid with a ball having radius $R$, consider following statements. A. Graph between terminal velocity V and R will be a parabola. B. The terminal velocities of different diameter balls are constant for a given liquid. C. Measurement of terminal velocity is dependent on the temperature. D. This experiment can be utilized to assess the density of a given liquid. E. If balls are dropped with some initial speed, the value of $\eta$ will change. Choose the correct answer from the options given below:
In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $\left[M^a L^b T^c\right]$. If $b=-3$, the value of $c$ is ________
For an experimental expression $y=\frac{32.3 \times 1125}{27.4}$, where all the digits are significant. Then to report the value of $y$ we should write
Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area $0.5 \mathrm{~m}^2$. It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is : $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$
Match List - I with List - II.  Choose the correct answer from the options given below :
Match the LIST-I with LIST-II $\begin{array}{|l|l|l|l|}\hline & \text{LIST-I} & & \text{LIST-II} \\ \hline \text{A.} & \text{Gravitational constant} & \text{I.} & {\left[\mathrm{LT}^{-2}\right]} \\ \hline \text{B.} & \begin{array}{l} \text{Gravitational potential} \\ \text{energy} \end{array} & \text{II.} & {\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right]} \\ \hline \text{C.} & \text{Gravitational potential} & \text{III.} & {\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]} \\ \hline \text{D.} & \begin{array}{l} \text{Acceleration due to} \\ \text{gravity} \end{array} & \text{IV.} & {\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]} \\ \hline \end{array}$ Choose the correct answer from the options given below :