JEE Main Physics — Mechanics previous year questions with solutions.
A soap bubble is blown to a diameter of $7 \mathrm{~cm} .36960 \mathrm{erg}$ of work is done in blowing it further. If surface tension of soap solution is $40 \mathrm{dyne} / \mathrm{cm}$ then the new radius is______ $\mathrm{cm}$ Take $\left(\pi=\frac{22}{7}\right)$
A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?
A small spherical ball of radius $r$, falling through a viscous medium of negligible density has terminal velocity $v$. Another ball of the same mass but of radius $2r$, falling through the same viscous medium will have terminal velocity:
A small liquid drop of radius $R$ is divided into $27$ identical liquid drops. If the surface tension is $T$, then the work done in the process will be :
A small ball of mass $m$ and density $\rho$ is dropped in a viscous liquid of density $\rho_0$. After sometime, the ball falls with constant velocity. The viscous force on the ball is :
A simple pendulum of length $1m$ has a wooden bob of mass $1\mathrm{kg}$. It is struck by a bullet of mass ${10}^{-2}\mathrm{kg}$ moving with a speed of $2\times {10}^{2}m{s}^{-1}$. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use $g=10m{s}^{-2}$)
A simple pendulum doing small oscillations at a place $\mathrm{R}$ height above earth surface has time period of $T_1=4 \mathrm{~s}$. $T_2$ would be it's time period if it is brought to a point which is at a height $2 \mathrm{R}$ from earth surface. Choose the correct relation $[R=$ radius of earth $]$ :
A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is : $\left(\right.$ Given $=$ Radius of geo-stationary orbit for earth is $4.2 \times 10^4 \mathrm{~km}$ )
A satellite of $10^3 \mathrm{~kg}$ mass is revolving in circular orbit of radius $2 R$. If $\frac{10^4 R}{6} J$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius (use $g=10 \mathrm{~m} / \mathrm{s}^2, R=$ radius of earth)
A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is $\frac{7}{x}$, where $x$ is ______.
A player caught a cricket ball of mass $150 \mathrm{~g}$ moving at a speed of $20 \mathrm{~m} / \mathrm{s}$. If the catching process is completed in $0.1 \mathrm{~s}$, the magnitude of force exerted by the ball on the hand of the player is:
A planet takes $200$ days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution?
A plane is in level flight at constant speed and each of its two wings has an area of $40{m}^{2}.$ If the speed of the air is $180\mathrm{km}{h}^{-1}$ over the lower wing surface and $252\mathrm{km}{h}^{-1}$ over the upper wing surface, the mass of the plane is ________$\mathrm{kg}.$ (Take air density to be $1\mathrm{kg}{m}^{–3}$ and $g=10m{s}^{–2}$)
A physical quantity $Q$ is found to depend on quantities $a,b,c$ by the relation $Q=\frac{{a}^{4}{b}^{3}}{{c}^{2}}$. The percentage error in $a,b$ and $c$ are $3%,4%$ and $5%$ respectively. Then, the percentage error in $Q$ is:
A physical quantity $Q$ is found to depend on quantities $a,b,c$ by the relation $Q=\frac{{a}^{4}{b}^{3}}{{c}^{2}}$. The percentage error in $a,b$ and $c$ are $3%,4%$ and $5%$ respectively. Then, the percentage error in $Q$ is:
A particle starts from origin at $t=0$ with a velocity $5\hat{i}m{s}^{-1}$ and moves in $x-y$ plane under action of a force which produces a constant acceleration of $(3\hat{i}+2\hat{j})m{s}^{-2}$. If the $x$-coordinate of the particle at that instant is $84m$, then the speed of the particle at this time is $\sqrt{\alpha }m{s}^{-1}$. The value of $\alpha$ is _______.
A particle of mass $m$ projected with a velocity $u$ making an angle of $30^{\circ}$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height $h$ is :
A particle of mass $m$ moves on a straight line with its velocity increasing with distance according to the equation $v=\alpha \sqrt{x}$, where $\alpha$ is a constant. The total work done by all the forces applied on the particle during its displacement from $x=0$ to $x=\mathrm{d}$, will be :
A particle moving in a straight line covers half the distance with speed $6 \mathrm{~m} / \mathrm{s}$. The other half is covered in two equal time intervals with speeds $9 \mathrm{~m} / \mathrm{s}$ and $15 \mathrm{~m} / \mathrm{s}$ respectively. The average speed of the particle during the motion is :
A particle moving in a circle of radius $R$ with uniform speed takes time $T$ to complete one revolution. If this particle is projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it is equal to $4R$. The angle of projection $\theta$ is then given by :
A particle moves in $x-y$ plane under the influence of a force $\vec{F}$ such that its linear momentum is $\overrightarrow{\mathrm{p}}(\mathrm{t})=\hat{i} \cos (\mathrm{kt})-\hat{j} \sin (\mathrm{kt})$. If $\mathrm{k}$ is constant, the angle between $\overrightarrow{\mathrm{F}}$ and $\overrightarrow{\mathrm{p}}$ will be :
A particle moves in $x-y$ plane under the influence of a force $\vec{F}$ such that its linear momentum is $\overrightarrow{\mathrm{p}}(\mathrm{t})=\hat{i} \cos (\mathrm{kt})-\hat{j} \sin (\mathrm{kt})$. If $\mathrm{k}$ is constant, the angle between $\overrightarrow{\mathrm{F}}$ and $\overrightarrow{\mathrm{p}}$ will be :
A particle moves in a straight line so that its displacement $x$ at any time $t$ is given by $x^2=1+t^2$. Its acceleration at any time $\mathrm{t}$ is $x^{-\mathrm{n}}$ where $\mathrm{n}=$ ___________
A particle is placed at the point $A$ of a frictionless track $\mathrm{ABC}$ as shown in figure. It is gently pushed towards right. The speed of the particle when it reaches the point $B$ is: $($Take $g=10m{s}^{-2})$. 