JEE Main Physics — Mechanics previous year questions with solutions.
Four identical solid spheres each of mass $m$ and radius $a$ are placed with their centres on the four corners of a square of side $b$. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :
Statement I: If three forces ${\vec{F}}_{1},{\vec{F}}_{2}$ and ${\vec{F}}_{3}$ are represented by three sides of a triangle and $\vec{{F}_{1}}+\vec{{F}_{2}}=-{\vec{F}}_{3},$ then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement II: A triangle made up of three forces $\vec{{F}_{1}},\vec{{F}_{2}}$ and $\vec{{F}_{3}}$ as its sides were taken in the same order, satisfies the condition for translatory equilibrium. In the light of the above statements, choose the most appropriate answer from the options given below:
The length of metallic wire is ${l}_{1}$ when tension in it is ${T}_{1}$. It is ${l}_{2}$ when the tension is ${T}_{2}$. The original length of the wire will be :
A physical quantity $y$ is represented by the formula $y={m}^{2}{r}^{-4}{g}^{x}{l}^{-\frac{3}{2}}$ If the percentage errors found in $y,m,r,l$ and $g$ are $18,1,0.5,4$ and $p$ respectively, then find the value of $x$ and $p$.
Three particles $P,Q$ and $R$ are moving along the vectors $\vec{A}=\hat{i}+\hat{j},\vec{B}=\hat{j}+\hat{k}$ and $\vec{C}=-\hat{i}+\hat{j}$, respectively. They strike on a point and start to move in different directions. Now particle $P$ is moving normal to the plane which contains vector $\vec{A}$ and $\vec{B}.$ Similarly particle $Q$ is moving normal to the plane which contains vector $\vec{A}$ and $\vec{C}.$ The angle between the direction of motion of $P$ and $Q$ is ${\mathrm{cos}}^{-1}(\frac{1}{\sqrt{x}}).$ Then the value of $x$ is $.$
Statement-I : Two forces $(\vec{P}+\vec{Q})$ and $(\vec{P}-\vec{Q})$ where $\vec{P}\perp \vec{Q},$ when act at an angle ${\theta }_{1}$ each other, the magnitude of their resultant is $\sqrt{3({P}^{2}+{Q}^{2})},$ when they act at an angle ${\theta }_{2},$ the magnitude of their resultant becomes $\sqrt{2({P}^{2}+{Q}^{2})}.$ This is possible only when ${\theta }_{1}<{\theta }_{2}.$<br>Statement-II : In the situation given above.<br>${\theta }_{1}=60^{\circ}$ and ${\theta }_{2}=90^{\circ}$<br>In the light of the above statement, choose the most appropriate answer from the options given below :
A boy pushes a box of mass $2\mathrm{kg}$ with a force $\vec{F}=(20\hat{i}+10\hat{j})N$ on a frictionless surface. If the box was initially at rest, then _______ $m$ is displacement along the $x$-axis after $10s$
A large number of water drops, each of radius $r$, combine to have a drop of radius $R$. If the surface tension is $T$ and mechanical equivalent of heat is $J$, the rise in heat energy per unit volume will be:
Three particles $P,Q$ and $R$ are moving along the vectors $\vec{A}=\hat{i}+\hat{j},\vec{B}=\hat{j}+\hat{k}$ and $\vec{C}=-\hat{i}+\hat{j}$, respectively. They strike on a point and start to move in different directions. Now particle $P$ is moving normal to the plane which contains vector $\vec{A}$ and $\vec{B}.$ Similarly particle $Q$ is moving normal to the plane which contains vector $\vec{A}$ and $\vec{C}.$ The angle between the direction of motion of $P$ and $Q$ is ${\mathrm{cos}}^{-1}(\frac{1}{\sqrt{x}}).$ Then the value of $x$ is $.$
The coefficient of static friction between a wooden block of mass $0.5\mathrm{kg}$ and a vertical rough wall is $0.2.$ The magnitude of the horizontal force that should be applied on the block to keep it adhere to the wall will be______$N$. $⌈g=10m{s}^{-2}]$
If the length of the pendulum in pendulum clock increases by $0.1%$, then the error in time per day is:
The area of cross-section of a railway track is $0.01{m}^{2}.$ The temperature variation is $10^{\circ}C.$ Coefficient of linear expansion of material of track is ${10}^{-5}C-1\circ .$ The energy stored per meter in the track is $J{m}^{-1}.$ (Young's modulus of material of track is ${10}^{11}N{m}^{-2}$)
Two separate wires $A$ and $B$ are stretched by $2\mathrm{mm}$ and $4\mathrm{mm}$ respectively, when they are subjected to a force of $2N.$ Assume that both the wires are made up of same material and the radius of wire $B$ is $4$ times that of the radius of wire $A.$ The length of the wires $A$ and $B$ are in the ratio of $a:b.$ Then $\frac{a}{b}$ can be expressed as $\frac{1}{x}$, where $x$ is _____.
The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ}$ and $48^{\circ}$ with the horizontal are ${R}_{1},{R}_{2}$ and ${H}_{1},{H}_{2}$ respectively. Choose the correct option:
Two narrow bores of diameter $5.0\mathrm{mm}$ and $8.0\mathrm{mm}$ are joined together to form a $U-$shaped tube open at both ends. If this $U-$tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water $T=7.3\times {10}^{-2}N{m}^{-1}$, angle of contact $=0,g=10{ms}^{-2}$ and density of water$=1.0\times {10}^{3}\mathrm{kg}{m}^{-3}]$
Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes $0.01{\mathrm{cm}}^{3}$ of oleic acid per ${\mathrm{cm}}^{3}$ of the solution. Then you make a thin film of this solution (monomolecular thickness) of area $4{\mathrm{cm}}^{2}$ by considering $100$ spherical drops of radius ${(\frac{3}{40\pi })}^{\frac{1}{3}}\times {10}^{-3}\mathrm{cm}.$ Then the thickness of oleic acid layer will be $x\times {10}^{-14}m$. Where $x$ is ________ .
The pressure acting on a submarine is $3\times {10}^{5}\mathrm{Pa}$ at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be: (Assume that atmospheric pressure is $1\times {10}^{5}\mathrm{Pa}$ density of water is ${10}^{3}\mathrm{kg}{m}^{-3},g=10{\mathrm{ms}}^{-2}$)
The radius of a sphere is measured to be $(7.50\pm 0.85)\mathrm{cm}$. Suppose the percentage error in its volume is $x$. The value of $x$, to the nearest $x$, is ___ .
A force of $F=(5y+20)\hat{j}N$ acts on a particle. The work done by this force when the particle is moved from $y=0m$ to $y=10m$ is ________$J$.
A swimmer can swim with velocity of $12\mathrm{km}/h$ in still water. Water flowing in a river has velocity $6\mathrm{km}/h$. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ________$^{\circ}$. (Round off to the Nearest Integer) (find the angle in degree)
If $\vec{P}\times \vec{Q}=\vec{Q}\times \vec{P}$, the angle between $\vec{P}$ and $\vec{Q}$ is $\theta (0^{\circ}<\theta <360^{\circ})$. The value of $\theta$ will be ___$^{\circ}$.
A block moving horizontally on a smooth surface with a speed of $40m{s}^{-1}$ splits into two parts with masses in the ratio of $1:2.$ If the smaller part moves at $60m{s}^{-1}$ in the same direction, then the fractional change in kinetic energy is :
Two wires of same length and radius are joined end to end and loaded. The Young's moduli of the materials of the two wires are ${Y}_{1}$ and ${Y}_{2}$. The combination behaves as a single wire then its Young's modulus is:
A porter lifts a heavy suitcase of mass $80\mathrm{kg}$ and at the destination lowers it down by a distance of $80\mathrm{cm}$ with a constant velocity. Calculate the work done by the porter in lowering the suitcase. (take $g=9.8{\mathrm{ms}}^{-2}$ )