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A block of mass $2\text{kg}$ is put on a rough horizontal surface having coefficient of friction $0.5$. The acceleration of block and frictional force acting on block if $F=5\text{N}$ is (Take $g=10{\text{m/s}}^2$)

A small block of mass $2\text{kg}$ having a velocity of $50\text{m/s}$ hits a larger block of mass $10\text{kg}$ initially at rest. The collision is perfectly inelastic and the smaller block sticks to the larger block. Find the velocity of the combined mass after the collision.

Four charges each of $+\frac{10}{3}\times {10}^{-9}C$ are placed at four corners of a square of side $8cm$. The potential at the intersection of the diagonals is

A bird flies for 4 s with a velocity of $|t-2|m/s$ in a straight line, where t = time in second. Find the distance it covers in metres.___

A particle starts from the origin of co-ordinates at time $t=0$ and moves in the $xy$ plane with a constant acceleration $\alpha$ in the $y$ – direction. Its equation of motion $y=\beta x^2$. Its velocity component in the $x$-direction is

A person can hear sound waves in the frequency range 20 Hz to 20 kHz. Find the minimum and the maximum wavelengths of sound that is audible to the person. The speed of sound is $360m^{-1}$.

The total revenue in rupees received from the sale of x units of a product is given by $R\left(x\right)=13x^2+26x+15$, Find the marginal revenue when x=7

A stone $A$ is dropped from rest from height $h$ above the ground. A second stone $B$ is simultaneously thrown vertically up from a point on the ground with velocity $v$. Find $v$ so that $B$ meets $A$ midway between their initial positions.

Two rods of equal length $\left(L\right)$ and equal mass $\left(M\right)$ are kept along $x$ and $y$ axis respectively such that their centres of mass lie at the origin. The moment of inertia about the line $y=x$, is

Which of the following parameters are required to express a vector quantity?

The knee voltage of a-n junction diode is 0.8 V and the with of the depletion layer is 2 μm. What is the electric field in the depletion layer?

For the expression $2x^2–7x-5$, the roots are α and β, then the value of α+β is

A student performs experiment with simple pendulum and measures time for 10 vibrations . If he measures time for 100 vibrations , the relative error in measurements of time period will be reduced by

A boggy of uniformly moving train is suddenly detached from train and stops after covering some distance. The ratio of distance covered by the boggy and distance covered by the train when the boggy has stopped is

A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillations with a time period T. If the mass is increased by m then the time period becomes $\left(\frac{5}{4}T\right)$ . The ratio of $\frac{m}{M}$ is

When a dielectric slab is introduced between the parallel plate capacitor, its capacitance

In uniform circular motion, the velocity vector and acceleration vector are

The horizontal range of a projectile is $4\sqrt{3}$ times its maximum height. Its angle of projection will be

A man weighs 70 kg. He stands on a weighing scale in a lift which is moving upwards with an acceleration of 5ms².What would be the reading on the scale? (g=10 ms²).

A $70\text{kg}$ man stands in contact against the inner wall of a hollow cylindrical drum of radius $3\text{m}$ rotating about its vertical axis. The coefficient of friction between the wall and his clothing is $0.15$. What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?

A body is executing simple harmonic motion. At a displacement x, its potential energy is $E_1$ and at a displacement y, its potential energy is $E_2$. The potential energy E at a displacement (x + y) is

The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately

For photoelectric emission, tungsten requires light of $2300\stackrel{\circ }{A}$. If light of $1800\stackrel{\circ }{A}$ wavelength is incident then emission

A body, constrained to move in the y-direction is subjected to a force given by $\overrightarrow{F}=(-2\hat{i}+15\hat{j}+6\hat{k})$ $\text{N}$. What is the work done by this force in moving the body a distance of $10\text{m}$ along the y-axis?

A Young's double slit interference arrangement with slits $S_1$and $S_2$is immersed in water (refractive index = 4/3) as shown in the figure. The positions of maxima on the surface of water are given by $x^2=p^2{m}^2{\lambda }^2-d^2$, where $\lambda$ is the wavelength of light in air (refractive index = 1), $2d$ is the separation between the slits and $m$ is an integer. The value of $p$ is

Figure shows two blocks in contact sliding down an inclined surface ofinclination 30${}^{\circ }$. The friction coefficient between the block of mass 2.0 kg and the incline is $\mu$${}_1$, and that between the block of mass 4.0 kg and the incline is $\mu$${}_2$. Calculate the acceleration of the 2.0 kg block if (a) $\mu$${}_1$ = 0.20 and $\mu$${}_2$ = 0.30, (b) $\mu$${}_1$ = 0.30 and $\mu$${}_2$ = 0.20. Take g = 10 m/s${}^2$.

If nitrogen gas molecules goes straight up with its rms speed at $0^{\circ }$ from the surface of the earth and there are no collision with other molecules, then it will rise to an approximate height of
(Take $g=10m/s^2$)

Suppose the smaller pulley of the previous problem has its radius 5.0 cm and moment of inertia $0.10kg-m^2$. Find the tension in the part of the string joining the pulleys.

A block slides down an inclined surface of inclination ${30}^{\circ }$ with the horizontal. Starting from rest it covers 8 m in the first two seconds. Find the coefficient of kinetic friction between the two.

A block of mass 2 kg is pushed against a rough vertical wall with a force of 40 N, coeffirient of static friction being 0.5 Another horizontal force of 15, is applied on the block iin the direction parallel to the wall. Will the block move? if yes, in which direction? If no, Find the frictional force exerted by the wall on the block.

How the force of attraction between two bodies varies with distance between them ?

Spherical cavity of spherical conductor has point $A$ inside conductor at distance $r$ from charge $Q$ & point $B$ is also inside conductor at distance $2r$ from charge $Q$, then

The range of a particle when launched at an angle of ${15}^{\circ }$ with the horizontal is $1.5km$. What is the range of the projectile when launched at an angle of ${45}^{\circ }$ to the horizontal?

Why longer wavelength does not always correspond to alpha lines???

Mention the reason please

Two thin long parallel wires separated by a distance b are carrying a current i ampere each. The magnitude of the force per unit length exerted by one wire on the other is

Figure here shows P and Q as two equally intense coherent sources emitting radiations of wavelength 20 m. The separation PQ is 5.0 m and phase of P is ahead of the phase of Q by ${90}^{\circ }$. A, B and C are three distant points of observation equidistant from the midpoint of PQ. The intensity of radiations at A, B, C will bear the ratio

[NSEP 1994]

A particle starts moving from rest from a fixed point in a fixed direction. The distance $s$ from the fixed point at a time $t$ is given by $s=t^2+at-b+17,$ where $a,b$ are real numbers. If the particle comes to rest after $5$ sec at a distance of $s=25$ units from the fixed point, then values of $a$ and $b$ are respectively

For sound waves in air with frequency 1000 Hz, a displacement amplitude of $1.2\times {10}^{-8}$ m produces a pressure amplitude of $3.0\times {10}^{-2}$ Pa. What is the wavelength of these waves? (Provided Bulk modulus of Air = $1.42\times {10}^{5}Pa$)