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Two equal forces (P each) act at a point inclined to each other at an angle of ${120}^0$ . The magnitude of their resultant is

If the mass of block is $m=32.96kg$ and the volume of block is $16m^3$, then the density of material will be (upto only two significant digit)

An open pipe of sufficient length is dipping in water with a speed $v$ vertically. If at any instant $l$ is length of tube above water. Then the rate at which fundamental frequency of pipe changes is
(speed of sound $=c$)

Find the force exerted by spring on the wedge shown in the figure. Assume that mass $\text{M}$ is in equilibrium (all surfaces are smooth).Take $g=10{\text{m/s}}^2$.

A parallel-plate capacitor has plates of area $A$ and separation $d$ and is charged to a potential difference $V$. The charging battery is then disconnected and the plates are pulled apart until their separation is $2d$. What is the work required to separate the plates?

A 50 turn closely wound circular coil of radius 12 cm carries a current of 2.4 A, the field at center of coil is.

System shown in figure is released from rest. Pulley and spring is massless and friction is absent everywhere. The speed of $5\text{kg}$ block when $2\text{kg}$ block leaves contact with ground is (Take force constant of $5\text{kg}$ spring $k=40\frac{\text{N}}{\text{m}}$ and $g=10\frac{\text{m}}{{\text{s}}^2}$

In a $Cu$-voltameter, the mass deposited in $30s$ is ${}^{\prime }{m}^{\prime }$ $g$. If the time-current graph is shown in the following figure, what is the electrochemical equivalent of $Cu$?

A string of length 60 cm fixed at both end is vibrating in its 2nd overtone. If mass per unit length of string is 0.2 kg/m, tension in string is 80 N and maximum amplitude of standing wave is 0.5 cm, then maximum speed of any point of string is

A robber fires $100$ bullets of mass $100\text{gm}$ each from a machine gun, each at a speed of $500\text{m/s}$. If the first $40$ bullets are fired in $10\text{s}$, what is the average force exerted on the machine gun by the robber during this period?

An rms voltage of $110\text{V}$ is applied across a series circuit having a resistance $11\Omega$ and an impedance $22\Omega$. The power consumed is

Suppose a ${}_{88}^{226}Ra$ nucleus at rest and in ground state undergoes $\alpha$-decay to a ${}_{86}^{222}Rn$ nucleus in its excited state. The kinetic energy of the emitted $\alpha$ particle is found to be $4.44MeV$. ${}_{86}^{222}Rn$ nucleus then goes to its ground state by $\gamma$-decay. The energy of the emitted $\gamma$ photon is $keV$.

[Given : atomic mass of ${}_{88}^{226}Ra=226.005u$, atomic mass of ${}_{86}^{222}Rn=222.000u$, atomic mass of $\alpha$ particle = $4.000u,1u=931MeV/c^2,c$ is speed of light]

Consider a book lying on a table. The weight of the book and the normal force by the table on the book are equal in magnitude and opposite in direction. Is this an example of Newton's third law?

During an inelastic collision there is loss of kinetic energy of the system then why there is no loss in total momentum of the system ?

Explain the meaning of the below sentence.
"The step size is thus very small as compared to the charges usually found and in many cases, we can assume a continuous charge variation."

In the figure the reading of the spring balance will be $:[g=10\frac{m}{s^2}]$

If E is the electric field intensity and ${\mu }_0$ is the permeability of free space, then the quantity $\frac{E^2}{{\mu }_0}$ has the dimensions of

Find the maximum value of $F$ such that the system is moving together. Take $g=10{\text{m/s}}^2$.

2 equal charges are kept at a certain distance from each other. The force on one of the charges is measured to be F. If the magnitude of one of the charge is increased by a factor of 3, what is the magnitude of the new force felt by the first charge?

In the equilibrium arrangement as shown, tension $T_2$ is $(g=10{\text{m/s}}^2)$

A ball is dropped from a bridge $122.5\text{m}$ high. After the first ball has fallen for $2$ second, a second ball is thrown straight down after it, what must be the initial velocity of the second ball, so that both the balls hit the surface of water at the same time?

Three forces acting on a body are shown in the figure. To have the resultant force only along the $y-$ direction, the magnitude of the minimum additional force needed is

The radiation from the sun, incident normally at the surface of the earth is $20{\text{kcal/m}}^2\text{min}$. What would have the radiant energy, incident normally on the earth, if the sun had a temperature twice of the present one?

Consider a small metallic plate of chromium, having only 5 free electrons on the surface. We shine light on the plate and we observe that these electrons come out but with different energies.

The energy received by each electron is 10 eV. Below is the list of energies with which each electron comes out.

e1 = 2.5 eV.

e2 = 2.7 eV.

e3 = 4.5 eV.

e4 = 5.5 eV.

e5 = 4.7 eV.

If one of these electrons has most optimally used the energy provided to come out, then what could be the work function of the metal chromium?

If $\frac{a}{b}=\frac{6}{7}$, then value of $\frac{2a+7b}{2a-7b}$ is

A bimetallic strip is formed out of two identical length strips of which one is copper and the other is brass. The coefficient of linear expansion of the two metals are ${\alpha }_C$ and ${\alpha }_B$ . On heating, the temperature of the strip goes up by $\Delta T$ and the strip bends to form an arc of radius of curvature $R$, then which of the following is/are correct ?

Two projectiles $A$ and $B$ are thrown from the same point with velocities $v$ and $\frac{v}{2}$ respectively. If B is thrown at an angle ${45}^{\circ }$ with horizontal, what is the inclination of A with horizontal when their ranges are same?

A block of mass $10\text{kg}$ is moving with a uniform speed of $20\text{m/s}$ enters onto a rough surface of coefficient of friction $0.8$, the time taken by the block to come to rest is

A person completes half of his journey with speed $v_1$ and rest half with speed $v_2$. The average speed ($v_{avg})$ of the person is

A body at rest starts moving under the action of a constant force along a straight line. The instantaneous power developed by this force with time $\text{t}$ is correctly represented by

when hydrogen sample in ground state is bombarded then what potential is required to accelerate electron so that first paschen line is emitted

Describe how contact force like friction etc as well as chemical reaction are instances of electromagnetic force

A balloon with it's contents weighing 160N moving down with an acceleration of g/2 ms^{​​​​-2} . The mass removed from it so that the balloon moves up with an acceleration of g/3ms^-2 is

5 litre of benzene weighs

At what point is the slope of the curve $y=-x^3+3x^2+9x-27$ maximum? Also, find the maximum slope.

What is a coherent system of unit?

What is the principal of homogeneity of dimensions?

What are supplementary units?

The equation of a progressive wave is $y=0.03\sin 2\pi [\frac{t}{0.01}-\frac{x}{0.30}]$ here $x$ and $y$ are in metres and $t$ is in seconds. The velocity of propagation of the wave is

calculate the maximum number of emission lines produce when an electron in hydrogen atom drops from 7th orbit to ground state

A plane wave of monochromatic light falls normally on a uniform thin film of oil which covers a glass plate. The wavelength of sources can be varied continuously. Complete destructive refraction is observed for $\lambda =5000\dot{A}$ and $\lambda =7000\dot{A}$ and for no other wavelength in between. If $\mu$ of oil is 1.3 and that of glass is 1.5, the thickness of the film will be

The magnitude of the focal length of a diverging less is 20 cm. What is the power of this lens?

In figure, $CP$ represents a wavefront and $AO$ and $BP$, the corresponding two rays. Find the condition on $\theta$ for constructive interference at P between the ray BP and reflected ray $OP$.

How exactly does the nature of a metal surface affect the work function?

What is the excess pressure inside a bubble of soap solution of radius 5.00 mm, given that the surface tension of soap solution at the temperature $\left({20}^{\circ }C\right)$ is $2.50\times {10}^{–2}N{m}^{–1}$? If an air bubble of the same dimension were formed at depth of 40.0 cm inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble? (1 atmospheric pressure is $1.01\times {10}^{5}Pa)$.

Paint gun depends upon:

Position vector of a particle is given as $\overrightarrow{r}=(\frac{4}{3}{t}^{\frac{3}{2}}\hat{i}-\frac{t^2}{2}\hat{j}+2t\hat{k})m$. Magnitude of acceleration at $t=1\text{sec}$ is: