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If the system is initially at rest. Find the acceleration of $2kg$ and $4kg$ masses, where it is given that $2kg$ mass does not slide on $4kg$ mass for the figure shown. The external force $F$ acting on the mass $2kg$ at an angle $\theta ={37}^{\circ }$. (Take $g=10m/s^2$)

Find the total energy stored between two concentric charged spherical shells of radii R and 2R and charge 2Q & -Q respectively.

Ans : 5Q^2/ 16pi epsilon0 R

Please give detailed explanation as I won't be able to understand concise answers.

The design value of lateral friction coefficient of highway is

In Bohr model of the hydrogen atom, the lowest orbit corresponds to

From a point at some height one body is dropped, while a second body is thrown downward with an initial velocity of $1{\text{ms}}^{-1}$ simultaneously in the same vertical line. The separation between these is $1.8\text{m}$ after a time

A man standing stationary with respect to a horizontal conveyer belt which is accelerating with $1{\text{m/s}}^2$ as shown in figure. If the coefficient of static friction between man's shoes and the belt is $0.2$, up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Mass of the man $=65\text{kg}$). Take $g=10{\text{m/s}}^2$.

A spherical conductor of radius $10\text{cm}$ has a charge of $3.2\times {10}^{-7}\text{C}$ distributed uniformly. What is the magnitude of electric field at point $15\text{cm}$ from centre of sphere$?$

$(\frac{1}{4\pi {ϵ}_0}=\text{9}\times {\text{10}}^{\text{9}}\text{N}{\text{m}}^2/{\text{C}}^2)$

A solid cylinder of mass $m$ is kept in balance on a fixed incline of angle $\alpha ={37}^{\circ }$ with the help of a thread fastened to its jacket. The cylinder does not slip. What will be the value of force $F$ that is required to keep the cylinder in balance when the thread is held vertically?

For a coil, inductive reactance is equal to its resistance, at certain frequency. Then the phase difference between voltage and current in radian is

The power factor of the circuit shown in the figure is $\frac{1}{\sqrt{2}}$. The capacitance of the circuit is equal to

All bulbs consume same power. The resistance of bulb $1$ is $36\Omega$.





$\left(ii\right)$ What is the voltage output of the battery , if the power of each bulb is $4\text{W}?$

The short-wavelength limit shifts by $26\text{pm}$ when the operating voltage in an X-ray tube is increased to $3$ times the original value. What was the original value of the operating voltage?

Four particles $\text{A, B, C}$ and $\text{D}$ each of mass $m$ are kept at the corners of a square of side $L$. Now the particle $\text{D}$ is taken to infinity by an external agent keeping the other particles fixed at their respective positions. The work done by the gravitational force acting on the particle $\text{D}$ during its movement is

Density of ice is $\rho$ and that of water is $\sigma$. What will be the decrease in volume when a mass M of ice melts

If $\overrightarrow{F}=\hat{i}{F}_x+\hat{j}{F}_y+\hat{k}{F}_z$ is conservative, then

1. 5

A hemispherical bowl just floats without sinking in a liquid of density 1.2 $\times$ ${10}^3$ kg/ $m^3$.. If outer diameter and the density of the bowl are 1 m and 2 $\times {10}^{4}Kg/m^3$ respectively, then the inner diameter of the bowl will be

The resultant of two forces $3P$ and $2P$ is $R.$ If first force is doubled then the resultant is also doubled. The angle between the forces is

Lift A is going up with velocity 20 m/s and acceleration a equal to $8m/s^2$ in the downward direction. While lift B is going down with 10 m/s and acceleration of +2$m/s^2$ in upward direction. At this moment a bolt in the ceiling of lift A gets loose and falls. Height of the lift is 16 m. Find the time taken by bolt to hit the floor of A.

1. 8

The velocity $v$ of a particle as a function of its position $\left(x\right)$ is expressed as $v=\sqrt{c_1-c_{2}x}$, where $c_1$ and $c_2$ are positive constants. The acceleration of the particle is

If $\overrightarrow{A}+\overrightarrow{B}$ is a unit vector along x - axis and $\overrightarrow{A}=\hat{i}-\hat{j}+\hat{k}$, then what is $\overrightarrow{B}$?

A particle is moved along a path $AB-BC-CD-DE-EF-FA$, as shown in figure in presence of a force $\overrightarrow{F}=(\alpha y\hat{i}+2\alpha x\hat{j})N$, where x and y are in meter and $\alpha =-1N{m}^{-1}$. The work done on the particle by this force $\overrightarrow{F}$ will bejoule. (write up to two decimal places)

If time taken by the projectile to reach $\text{Q}$ is $T$, then what is the magnitude of $\text{PQ}$?

A satellite moving around earth at a height $R$ (radius of earth) from the surface of earth needs to be put into another circular orbit of radius $8R$. How much more energy needs to be provided to take the satellite to the new orbit? ($M_e$ is mass of the earth and $m$ is mass of satellite).

Read the following sentences

• The train steamed forward at full speed.

• The train headed for the steep mountains.

Find five more such words from the lesson.

Potential at the centroid of an equilateral triangle of side ‘a’, when equal charges each of magnitude ‘Q’ are placed at the vertices of the triangle is?