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A block of mass $m$ rests on a rough horizontal surface as shown in the figure. Coefficient of friction between the block and the surface is $\mu$. A force $F=mg$ acting at angle $\theta$ with the vertical side of the block pulls it. In which of the following cases can the block be pulled along the surface?

The point B lies on a smooth plane inclined at ${30}^{\circ }$ to the horizontal. A particle of mass $\frac{1}{7}\text{kg}$ is dropped from a point A which lies $10\text{m}$ vertically above B. The particle rebounds from the plane in the direction BC with speed $v\text{m/s}$ at an angle of ${45}^{\circ }$ to the plane. Find the impulse exerted by the plane on the particle (in $\text{Ns}$)

An electric fan has blades of length 30 cm as measured from the axis of rotation. If the fan is rotating at 1200 r.p.m. The acceleration of a point on the tip of the blade is about

Calculate the stress in a tight wire of a material whose young’s modulus is $19.6\times {10}^{11}dyne/c{m}^2$, so that the speed of the longitudinal wave is 20 times the speed of transverse wave.

Monochromatic light of wavelength of 600nm is used in a YDSE. One of the slits is covered by a transparent sheet of thickness $1.8\times {10}^{-5}m$ made of a material of refractive index 1.6. How many fringes will shift due to the introduction of the sheet?

A spherical body of radius $b=\frac{4}{\pi }\text{m}$ has a concentric cavity of radius $a=\frac{2}{\pi }\text{m}$ as shown. Thermal conductivity of the material is $100{\text{W/m}}^{\circ }\text{C}$. Find the thermal resistance between inner and outer surface.

The angle of prism is $3^{\circ }$. The refractive index is $1.5$. The angle of minimum deviation is .

For an isobaric process involving an ideal gas, the ratio of heat supplied and work done by the system (gas) is

A rod of length $L$ is pivoted at one end and is rotated with a uniform angular velocity in a horizontal plane. The value of $x$ for point $P$, where tension is ${\left(\frac{1}{4}\right)}^{th}$ of the tension at $O$

The axis of rotation of a purely rotating body

If force, $F=120N$ is acting parallel to the inclined plane, find tension $T$ in the string as shown in the figure. All surfaces are smooth.

(Take $g=10{\text{m/s}}^2$).

The top of insulated cylindrical container is covered by a disc having emissivity 0.6 and thickness 1 cm. The temperature is maintained by circulating oil as shown in figure. If temperature of upper surface of disc is ${127}^{\circ }$ Cand temperature of surrounding is ${27}^{\circ }$ C, then the radiation loss to the surroundings will be (Take $\sigma =\frac{17}{3}\times {10}^{-8}W/m^2{K}^4$)

A mercury arc lamp provides $0.1\text{W}$ of ultra-violet radiation at a wavelength of $\lambda =2537\stackrel{\circ }{A}$ only. The photo tube (cathode of photo electric device) consists of potassium and has an effective area of $4c{m}^2$. The cathode is located at a distance of $1\text{m}$ from the radiation source. The work function for potassium is ${\varphi }_0=2.2eV$.

What is the cut off potential $V_0$ ?

A Body moves 6 m north. 8 m east and 10m vertically upwards, what is the magnitude of its resultant displacement from initial position?

The operating temperature of the filament of lamp is $2000{}^{\circ }C$. The temperature coefficient of the material of filament is $0.005{}^{\circ }{C}^{-1}$. If the atmospheric temperature is $0{}^{\circ }C$, then the current in the $100W-200V$ lamp when it is switched on is nearest to

The electric field in a region is radially outward with magnitude $E=A{\gamma }_0$ . The charge contained in a sphere of radius ${\gamma }_0$ centered at the origin is

The refractive index of the core of an optical fiber is ${\mu }_2$ and that of the cladding is ${\mu }_1$. The angle of incidence on the face of the core so that the light ray just undergoes total internal reflection at the cladding is

Suppose the kinetic energy of a body oscillating with amplitude $A$ and at a distance $x$ is given by $K=\frac{Bx}{x^2+A^2}$. The dimensions of $B$ are the same as that of

If force, $F=48N$ is acting on the system as shown in figure, find the tension in string. All surfaces are smooth.

(Take $g=10m/s^2$)

The stopping potential $\left(V_0\right)$

A satellite of mass $1000kg$ is rotating around the earth in a circular orbit of radius $3R$. What extra energy should be given to this satellite, if it is to be lifted into an orbit of radius $4R$?

A particle (a mud pallet) of mass 'm' strikes a smooth stationary wedge of mass $M$ with a velocity $v_0$, at an angle $\theta$ with horizontal. If the collision is perfectly inelastic, find the velocity of the wedge just after the collision.

Time period of a satellite revolving above Earth’s surface at a height equal to R, where R the radius of Earth, is

For the situation shown in figure, match the following table.





$\begin{array}{cc}\text{Table -1}& \text{Table -2}\\ \text{(A)Absolute acceleration of}& \text{(P)}11{\text{m/s}}^2\\ \text{1 kg block}& \\ \text{(B)Absolute acceleration of}& \text{(Q)}6{\text{m/s}}^2\\ \text{2 kg block}& \\ \text{(C)Relative acceleration between}& \text{(R)}17{\text{m/s}}^2\\ \text{the two blocks}& \\ & \text{(S) None}\end{array}$

Find $B_0$

Find the total energy of the capacitors present in the circuit given below

Two bodies of masses $3\text{kg}$ and $6\text{kg}$ possess kinetic energies of $6\text{J}$ and $10\text{J}$ respectively. What is the ratio of their linear momentum?

A student is standing at a distance of 50 metres from the bus. As soon as the bus starts its motion with an acceleration of $1{\text{m/s}}^2$ , the student starts running towards the bus with an uniform velocity $u$. Assuming the motion to be along a straight road, the minimum value of $u$, so that the student is able to catch the bus is

The frequency and intensity of a light source are both doubled. Consider the following statements.

A. The saturation photocurrent remains almost the same

B. The maximum kinetic energy of the photoelectrons is doubled

If a boat can go with a maximum velocity of 40 km/hr with respect to water in a pond, then what will be the boat's maximum velocity with respect to water in a river flowing at 20 km/hr.



(i) upstream (ii) downstream respectively.

Three particles $A,B$ and $C$ are situated at the vertices of an equilateral triangle $ABC$ of side $d$ at $t=0$. Each of the particles moves with constant speed $v$. $A$ always has its velocity along $AB$ i.e. along the line joining the two particles, $B$ along $BC$ and $C$ along $CA$. At what time will the particles meet each other?

The acceleration- time graph of a particle moving along a straight line is as shown in figure. At what time the particle acquires its initial speed?

In the figure shown, a liquid is flowing through a tube at the rate of 0.1 $m^3$/sec. The tube is randed into two semicircular tubes of cross sectional area $\frac{A}{3}$ and 2$\frac{A}{3}$. The velocity of liquid at Q is $V_Q$ and Velocity at P is $V_P$ (The cross-sectional area of the main is A)

A conductor lies along the $z$-axis at$–1.5\le z\le 1.5\text{m}$ and carries a fixed current of $10.0\text{A}$ in $–\hat{k}$ direction (see figure). For a field $\overrightarrow{B}=3.0\times {10}^{-4}{e}^{0.2x}\hat{j}\text{T}$, find the power required to move the conductor at a constant speed to $x=2.0\text{m}$, $y=0\text{m}$ in $5\times {10}^{–3}\text{s}$. Assume parallel motion along the $x$-axis. (Assume $e^{0.4}=1.5$)

A simple pendulum has a time period $T$ in vacuum. Its time period when it is completely immersed in a liquid of density one-eighth of the density of the material of the bob is

A rod of length $10\text{cm}$ lies along the principal axis of a concave mirror of focal length $10\text{cm}$ in such a way that its end close to the pole is $20\text{cm}$ away from the mirror. The length of the image is

A plate of thickness t made of a material of refractive index $\mu$ is placed in front of one of the slits in a double-slit experiment. What should be the minimum thickness t which will make the intensity at the centre of the fringe pattern zero?

For CE transistor amplifier, the audio signal voltage across the collector resistance of $2k\Omega$ is 4V. If the current amplification factor of the transistor is 100 and the base resistance is $1k\Omega$, then the input signal voltage is

A block of mass $10\text{kg}$ is placed on rough horizontal surface whose coefficient of friction is $0.5$. If a horizontal force of $100\text{N}$ is applied on it, then acceleration of block will be [Take $g=10{\text{ms}}^{-2}$]

Man $A$ and $B$ come to the middle of a boat which is at rest. Then displacement of the boat (neglecting any kind of friction) will be

A thin brass sheet at ${10}^{\circ }C$ and a thin steel sheet at ${20}^{\circ }C$ have same surface area. The common temperature at which both would have the same area is :

Coefficient of areal expension for brass and steel are ${10\times {10}^{-6}}^{\circ }{C}^{-1}$ and ${20\times {10}^{-6}}^{\circ }{C}^{-1}$ respectively.

A wire of initial length $L$ and radius $r$ is stretched by a length $l$. Another wire of same material but with initial length $2L$ and radius $2r$ is stretched by a length $2l$. The ratio of the stored elastic energy per unit volume in the first and second wire is

Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to $R^{\frac{-5}{2}}$, and $T^2$ is proportional to

A linear simple harmonic oscillation has a total mechanical energy of $300\text{J}$. Its potential energy at mean position is $100\text{J}$. Find the minimum potential energy.