Physics Mechanics questions from JEE Main 2015.
A beaker contains a fluid of density $\rho$$\frac{kg}{{m}^{3}}$ , specific heat $S\frac{J}{k{g}^{o}C}$ and viscosity $\eta$ . The beaker is filled up to height h. To estimate the rate of heat transfer per unit area $(\frac{\overset{˙}{Q}}{A})$ by convection when beaker is put on a hot plate, a student proposes that it should depend on $\eta$ , $(\frac{S\Delta \theta }{h})$ and $(\frac{1}{\rho g})$ when $\Delta \theta$ ( ${in}^{o}C$ ) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for $(\frac{\overset{˙}{Q}}{A})$ is:
A block of mass $m=0.1 \mathrm{kg}$ is connected to a spring of unknown spring constant k. It is compressed to a distance $x$ from its equilibrium position and released from rest. After approaching half the distance $(\frac{x}{2})$ from the equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with velocity $3 m{s}^{-1}$. The total initial energy of the spring is:
A block of mass $m=10 \mathrm{kg}$ rests on a horizontal table. The coefficient of friction between the block and the table is $0.05$. When hit by a bullet of mass $50g$ moving with speed $v$, that gets embedded in it, the block moves and comes to stop after moving a distance of $2m$ on the table. If a freely falling object were to acquire speed $\frac{v}{10}$ after being dropped from height $H$, then neglecting energy losses and taking $g=10 m{s}^{-2}$, the value of $H$ is close to
A large number $(n)$ of identical beads, each of mass $m$ and radius $r$ are strung on a thin smooth rigid horizontal rod of length $L(L\gg r)$ and are at rest at random positions. The rod is mounted between two rigid supports (see figure). If one of the beads is now given a speed $v$, the average force experienced by each support after a long time is (assume all collisions are elastic): 
A particle is moving in a circle of radius $r$ under the action of a force $F=\alpha {r}^{2}$ which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy$=0$ for $r=0$):
A particle of mass $2\mathrm{kg}$ is on a smooth horizontal table and moves in a circular path of radius $0.6m$. The height of the table from the ground is $0.8m$. If the angular speed of the particle is $12 \mathrm{rad} {s}^{-1}$ , the magnitude of its angular momentum about a point on the ground right under the center of the circle is:
A particle of mass $\text{m}$ moving in the $x$ direction with speed $2v$ is hit by another particle of mass $2m$ moving in the $y$ direction with speed $v.$ If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to:
A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to ${T}_{M}$ . If the Young's modulus of the material of the wire is $Y$, then $\frac{1}{Y}$ is equal to: ($g=$gravitational acceleration)
A uniform solid cylindrical roller of mass $m$ is being pulled on a horizontal surface with force $F$ parallel to the surface and applied at its centre. If the acceleration of the cylinder is $a$ and it is rolling without slipping then the value of $F$ is:
A uniform thin rod AB of length $L$ has linear mass density $\mu (x)=a+\frac{bx}{L}$, where $x$ is measured from A. If the CM of the rod lies at a distance of $(\frac{7}{12}L)$ from A, then $a$ and $b$ are related as:
A vector $\vec{A}$ is rotated by a small angle $\Delta \theta$ radians $(\Delta \theta \ll 1)$ to get a new vector $\vec{B}$ . In that case $|\vec{B}-\vec{A}|$ is :
A very long (length $L$) cylindrical galaxy is made of uniformly distributed mass and has radius $R(R<<L)$. A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of the star is $T$ and its distance from the galaxy's axis is $r$, then
Consider a thin uniform square sheet made of a rigid material. If its side is $a$, mass m and moment of inertia $I$ about one of its diagonals, then:
Diameter of a steel ball is measured using a Vernier calipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its Vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as: <table class="pyq-table"><tbody><tr><td>S.No.</td><td>MS (cm)</td><td>VS divisions</td></tr><tr><td>1.</td><td>0.5</td><td>8</td></tr><tr><td>2.</td><td>0.5</td><td>4</td></tr><tr><td>3.</td><td>0.5</td><td>6</td></tr></tbody></table> If the zero error is - 0.03 cm, then mean corrected diameter is:
Distance of the centre of mass of a solid uniform cone from its vertex is ${z}_{0}$. If the radius of its base is $R$ and its height is $h$ then ${z}_{0}$ is equal to:
From a solid sphere of mass $M$ and radius $R$, a cube of the maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is:
From a solid sphere of mass $M$ and radius $R\text{,}$ a spherical portion of radius $(\frac{R}{2})$ is removed as shown in the figure. Taking gravitational potential $V=0$ at $r=\infty ,$ the potential at the centre of the cavity thus formed is ($G=$gravitational constant) 
From the top of a $64$ metres high tower, a stone is thrown upwards vertically with the velocity of $48 m/s.$ The greatest height (in metres) attained by the stone, assuming the value of the gravitational acceleration $g=32 m/{s}^{2}$, is:
If a body moving in a circular path maintains constant speed of $10 m{s}^{-1}$ , then which of the following correctly describes the relation between acceleration and radius?
If electronic charge $e$, electron mass $m$, speed of light in vacuum $c$ and Planck's constant $h$ are taken as fundamental quantities, the permeability of vacuum ${\mu }_{0}$ can be expressed in units of:
If the capacitance of a nanocapacitor is measured in terms of a unit $u$, made by combining the electronic charge $e$, Bohr radius ${a}_{0}^{},$ Planck's constant $h$ and speed of light $c$ then
If two glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is R and surface tension of water is T then the pressure in water between the plates is lower by: 
 Given in the figure are two blocks $A$ and $B$ of weight $20N$ and $100N$, respectively. These are being pressed against a wall by a force $F$ and kept in equilibrium as shown. If the coefficient of friction between the blocks is $0.1$ and between block $B$ and the wall is $0.15$, the frictional force applied by the wall on block $B$ is:
The period of oscillation of a simple pendulum is $T=2\pi \sqrt{\frac{l}{g}}.$ Measured value of $l$ is $20.0\mathrm{cm}$, known to $1\mathrm{mm}$ accuracy and time for $100$oscillations of the pendulum is found to be $90s$ using a wristwatch of $1s$ resolution. The accuracy in the determination of $g$ is
Two stones are thrown up simultaneously from the edge of a cliff $240m$ high with an initial speed of $10m{s}^{-1}$ and $40m{s}^{-1}$ respectively. Which of the following graph best represents the time variation of the relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance, take $g=10 {\mathrm{ms}}^{-2}$)(the figure are schematic and not drawn to scale)
Which of the following most closely depicts the correct variation of the gravitation potential, $V(r)$ with distance $r$ due to a large planet of radius $R$ and uniform mass density? (figures are not drawn to scale)