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A rubber rope of length $7\text{m}$ is hung from the ceiling of a room. What is the increase in length of the rope due to its own weight? (Given: Young's modulus of elasticity of rubber = $5\times {10}^6{\text{N m}}^{-2}$ and density of rubber = $1.5\times {10}^3\frac{\text{kg}}{{\text{m}}^3}$ and $g=10\frac{\text{m}}{{\text{s}}^2}$)

A spherical volume contains a uniformly distributed charge of volume density $2.0\times {10}^{-4}C{m}^{-3}$. Find the strength of electric field at a point inside the volume at a distance $4.0cm$ from the centre.

Twelve identical resistance are arranged to form a cubical structure find the effective resistance between .

1 and 2

Three particles A, B and C, each of mass m, are placed in a line with AB = BC = d. Find the gravitational force on a fourth particle P of same mass, placed at a distance d from the particle B on the perpendicular bisector of the line AC.

A bird fly east at $10\text{m/s}$ for $100\text{m}$. It then turns around flies at $20\text{m/s}$ for $15\text{s}$. Neglect time taken for turning, find its magnitude of average velocity.

A ray of light falls on the surface of a spherical glass paperweight making an angle $\alpha$ with the normal and is refracted in the medium at an angle $\beta$. The angle of deviation of the emergent ray from the direction of the incident ray

A solid sphere of mass $500\text{g}$ and radius $10\text{cm}$ rolls without slipping with a velocity of $20\text{cm/s}$. The total $K.E$. of the sphere is nearly

The Galvanometer works on the principle that the angle of turn of the device, $\theta$ is

Two springs of equal lengths and equal cross-sectional areas are made of materials whose Young's moduli are in the ratio of 3:2. They are suspended and loaded with the same mass. When stretched and released, they will oscillate with time periods in the ratio of

The equation of motion of a projectile are given by x = 36 t metre and $2y=96t–9.8t^2$ metre. The angle of projection is

The wavelength of K-alpha characteristic x-rays only depends upon:

A train travelling at $60\text{km/h}$ overtakes another train travelling at $42\text{km/h}$. Assuming each car to be $50\text{m}$ long and initially train $A$ to be just behind the train $B$, the total distance train A will cover to overtake train B is closest to

Given that $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C}$. If $|\overrightarrow{A}|=4,|\overrightarrow{B}|=5$ and $|\overrightarrow{C}|=\sqrt{61}$, then angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is:

If a body describes a circular motion under inverse square field, the time taken to complete one revolution, T is related to the radius of the circular orbit as

For a colour coded carbon resistance, initial three bands are red and fourth band is silver. Its resistance is

Motion described by two different objects are shown in the figure. The ratio of accleration of the objects i.e. $\frac{a_A}{a_B}$ is

A spherically symmetric gravitational system of particles has a mass density $\rho =\{\begin{array}{c}{\rho }_0\text{for}r\le R\\ 0\text{for}r>R\end{array}$

where ${\rho }_0$ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed $V$ as a function of distance $r(0<r<\infty )$ from the centre of the system is represented by

A uniform chain has a mass $M$ and length $L$. It is placed on a frictionless table with length $L_0$ hanging over the edge. The chain begins to slide down. Then, the speed $v$ with which the end slides down from the edge is given by

For given velocity-time graph, which of the following options represents correct acceleration-time graph?

What is the $y$ coordinate of the centre of mass of a semi-circular disc as shown in the figure? The smaller disc has been cut from the larger one. Consider the discs to have uniform density. Consider the axes and origin as shown in figure.

An aeroplane moving with 150 m/s drops a bomb from a height of 80 m so as to hit a target. What is the distance between the target and the point where the bomb is dropped? (given $g=10m/s^2$)

Find the value of acceleration of block $B$ (in ${\text{m/s}}^2$) for the system shown in figure. Take $g=10{\text{m/s}}^2$.

A block of mass $3\text{kg}$ is at rest on a rough inclined plane as shown in the figure. The magnitude of net force exerted by the surface on the block will be $(g=10{\text{m/s}}^2)$

A body of mass $2\text{kg}$ is hung on a spring balance mounted vertically in a lift. If the lift moves up with an acceleration equal to the acceleration due to gravity, the reading on the spring balance will be

The specific heat of argon at constant volume is $0.075\text{kcal/kg K}$. Calculate its atomic weight [ $R=2\text{cal/mol K}$ ]

The moment of inertia of a solid sphere about an axis passing through the centre of gravity is $\frac{2}{5}M{R}^2$; then its radius of gyration about a parallel axis at a distance $2R$ from first axis is

A glass marble whose mass is $200g$, falls from a height of $2.5m$ and rebounds to a height of $1.6m$. Find the impulse acting due to its fall

Two identical rods are joined as shown. The system is pivoted at point $O$ and is released from rest from the horizontal position. The speed of point $A$ when $OB$ become vertical is

In a school the physics teacher decides to perform an experiment in the lab. He left an ideal spring block system to do SHM an a frictionless table.

Five students are sent in the lab one by one and asked to write the equation of the SHM.

$Ram-{\Delta }_{0}sin(\omega t+\frac{\pi }{6})$

$Himanshu-{\Delta }_{0}sin(\omega t+\frac{2\pi }{3})$

$Satra-{\Delta }_{0}cos(\omega t+\frac{2\pi }{3})$

$Avinash-{\Delta }_{0}sin(\omega t+\frac{7\pi }{6})$

$Abhishek-{\Delta }_{0}sin(\omega t+\frac{5\pi }{6})$

Anand was asked to point out whose equations were in same phase and whose were in opposite phase?

(i)Ram and Avinash(x) same phase

(ii)Abhishek &Avinash(y) Opposite phase

(iii)Ram &Satra

Satra&Avinash

Two strings (fixed at both ends) $P$ and $Q$ of equal length, made of same material and vibrating in same mode produces beats of frequency $5\text{Hz}$. String $Q$ is vibrating at a frequency $460\text{Hz}$. If the tension in string $P$ increases, the beat frequency increases to $7\text{Hz}$. The initial frequency of vibration for string $P$ is :

If $T$ is the total time of flight, $h$ is the maximum height & $R$ is the range for horizontal motion, the $x$ and $y$ co-ordinates of projectile motion and time $t$ are related as:

What is the bulk modulus of oxygen if $32\text{g}$ of oxygen occupies $22.4\text{L}$ volume and the speed of sound in oxygen is $320\text{m/s}$ ?

A vehicle can accelerate or decelerate at a maximum value of $1m{s}^{-2}$ and can attain a maximum speed of $20m{s}^{-1}$. If it starts from rest, what is the shortest time in which it can travel $1000m$, in a straight path, if it has to come to rest at the end of $1000m$?

Two slabs each of area $A$, length $2\text{m}$ and $4\text{m}$, thermal conductivities $k_1=300{\text{W/m}}^{\circ }\text{C}$ and $k_2=200{\text{W/m}}^{\circ }\text{C}$ respectively are joined to form a single slab of length $6\text{m}$. Find the equivalent thermal conductivity of resultant slab. (in ${\text{W/m}}^{\circ }\text{C}$)

An iron rod of length $1\text{m}$ is fixed between two walls as shown in figure. Find thermal stress and thermal strain developed in the rod if it is heated by $\Delta T={20}^{\circ }C$

(Given: Coefficient of linear expansion of iron is $1.2\times {10}^{-5}{}^{\circ }{C}^{-1}$; Young's modulus of iron is $2\times {10}^{11}{\text{N/m}}^2$).

A horizontal platform is executing simple harmonic motion in the vertical direction with a frequency $v$. A block of mass $m$ is placed on the platform. What is the maximum amplitude of the platform so that the block is not detached from it?

The moment of inertia of a hollow cylinder of radius $R$ and mass $M$ about an axis passing through the outer circumference along the height of the hollow cylinder is

A wire loop enclosing a semicircle of radius $R$ is located on the boundary of uniform magnetic field $B$. At time $t=0$, the loop is set into motion with constant angular accleration $\alpha$ about an axis passing through $O$ and is perpendicular to semicircle. The clockwise emf direction is taken to be positive. The modulus of variation of emf as a function of time is ($0<\theta <\pi$)

Consider a drop of rain water having mass $1g$ falling from a height of $1km$. It hits the ground with a speed of $50m/s$. Take '$g$' constant with a value $10m/s^2$. The work done by the (i) gravitational force (ii) resistive force of air is

A particle tied to the end of a string oscillates along a circular arc in a vertical plane. The other end of the string is fixed at the centre of the circle. If the string has a breaking strength of twice the weight of the particle; (x) Find the maximum distance that the particle can cover in one cycle of oscillation. The length of the string is 50 cm. (y) Find the tension in the extreme position (z) Find the net acceleration of the particle at extreme

(i) $\frac{2\pi }{3}m$ (ii)$\frac{mg}{4}$ (iii) $g\sqrt{\frac{2}{3}}$ (iv)$\frac{mg}{2}$ (v)$\frac{\pi }{3}m$

(vi) $g\sqrt{\frac{3}{2}}$

Three resistances of magnitude $R$ each are connected in the form of an equilateral triangle of side $a$. The combination is placed in a magnetic field $B=B_0{e}^{-\lambda t}$ perpendicular to the plane. The induced current in the circuit is given by

One mole of an ideal monoatomic gas is taken through a cycle $a\to b\to c\to a$ as shown in the figure. Find the difference between maximum and minimum values of internal energy of the gas during the cycle.

If a hollow metal sphere is given a charge Q and another conducting sphere is placed inside it concentrically. A charge q is placed at the centre. The charge that appears on the surface B of the inner sphere is

There is a thin uniform disc of radius R and mass per unit area $\sigma$, in which a hole of radius R/2 has been cut out as shown in the figure. Inside the hole a square plate of same mass per unit area $\sigma$ is inserted so that its corners touch the periphery of the hole. Find centre of mass of the system distance from O.

A rotating mirror with uniform angular speed $\omega$ is placed at the centre $\left(C\right)$ of the sphere of radius $\left(R\right)$ as shown in the figure. Incident light falls on the mirror. The linear speed $\left(v\right)$ of the light spot on the sphere is

In the figure shown, a ring $A$ is initially rolling without sliding with a velocity $v$ on a horizontal surface of the body $B$ (of same mass as $A$). All surfaces are smooth. $B$ has no initial velocity. What will be the maximum height reached by $A$ on $B$?