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A block A of mass $5\text{kg}$ is placed on a table and connected to another block B of mass $3\text{kg}$ with a light string passing over a frictionless pulley. The coefficient of friction between the table the block A is $0.4$. The block B is suddenly dropped and the string breaks after $3$ seconds. What is the total distance covered by block A?

An object is projected upwards with a velocity of $100\text{m/s}$. It will strike the ground after

Four Charges $1\times {10}^{-8}C,-2\times {10}^{-8}C,3\times {10}^{-8},3\times {10}^{-8}$ are placed at the four corners of a square of side 1 m. The potential at the centre of the square is

A detector is released from rest over a source of sound of frequency $f_0={10}^3\text{Hz}$. The frequency observed by the detector at time $t$ is plotted in the graph. The speed of sound in air is $(g=10{\text{m/s}}^2)$

Find the derivative of $f\left(t\right)=\frac{4}{t}-\frac{1}{6t^3}+\frac{8}{t^5}$.

Six identical resistors each of $10\Omega$ are connected as shown in the figure. The equivalent resistance between points $\text{X}$ and $\text{Y}$ is :

During the adiabatic expansion of 2 moles of a gas, the internal energy of the gas is found to decrease by 2 joules, the work done during the process on the gas will be equal to

In the shown figure $m_A,m_{B}and{m}_C$ are the masses of the three blocks, the incline is frictionless $m_A=5kg,m_B=10kg,m_C=2kg$. coefficient of friction between A and B is 0.5 and between B and C is 0.1 (Take g = 10 $m/s^2$) On the basis of above data answer the following questions.

What is the tension in the rod ?

1. 100

The intensity of each of the two slits in Young's double slit experiment is $I_0$. Calculate the minimum separation between the two points on the screen where intensities are $2I_0$ and $I_0$. Given, the fringe width equal to $\beta$.

The period of simple pendulum inside a stationary lift is T. The lift accelerates upward with an acceleration of g/3.The time period of simple pendulum will be

Three identical bulbs are connected in series and these together dissipate a power $P$. If now these bulbs are connected in parallel, then the power dissipated will be

Angular velocity of a particle is $\omega =\frac{{\theta }^2}{2}$, where $\theta$ is angular position of particle. Tangential acceleration of particle when it has covered $1$ revolution in a circle of radius $2\text{m}$ is

The angular speed of a flywheel making $60\text{revolutions/minute}$ is

A charged particle of specific charge, $\alpha =\left(\frac{q}{m}\right)$ is released at origin at $t=0$ with velocity $v=v_0(\hat{i}+\hat{j})$ in a uniform magnetic field $B=B_0\hat{i}$. Coordinates of particle at time $t=\frac{\pi }{B_0\alpha }$ are:

A particle executes $\text{SHM}$ with an angular frequency $4\pi \text{rad/s}$. If it is at its positive extreme position initially, find the first instant when it is at a distance of $\frac{1}{\sqrt{2}}$ times its amplitude from the mean position in positive direction

Find the equivalent resistance between points $M$ and $N$ in the circuit shown in figure.

A spring of unstretched length $l$ and force constant $k$ is stretched by a small length $x$. It is further stretched by another small length $y$. The work done in the second stretching is

If I am pulling a block with a string and after a time t my displacement is x then what will be the displacement of the block in the same time duration?

An infinite number of charges, each numerically equal to $q$ and of the same sign, are placed along the x-axis at $x=1\text{m},x=2\text{m},x=4\text{m},x=8\text{m}$ and so on. Then the electrical potential at $x=0$ due to this set of charges is ( Assume that $\frac{1}{4\pi {ϵ}_0}=k$)

A uniformly charged thin spherical shell of radius R carries uniform surface charge density of $\sigma$ per unit area. It is made of two hemispherical shells, held together by pressing them with force F (see figure). F is proportional to