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A person trying to lose weight by burning fat filts a mass of \({10}{k}{g}\) upto a being of \({1}{m}{1000}\) time . Assume that the potential energy lost each time be lower the mass is dissipated . How much far will be use up considering the work done only when the weight is lifted up ? Far supplies \({3.8}\times{10}^{{{7}}}{J}\) of energy per kg wich is canverted to mechanical energy with \({x}{20}\%\) efficiency rate Take \(={9.8}{m}{s}^{{-{2}}}\)

(A) \({9.89}\times{10}^{{-{3}}}{k}{g}\)

(B) \({12.89}\times{10}^{{-{3}}}{k}{g}\)

(C) \({2.45}\times{10}^{{-{3}}}{k}{g}\)

(D) \({6.45}\times{10}^{{-{3}}}{k}{g}\)

(A) \({9.89}\times{10}^{{-{3}}}{k}{g}\)

(B) \({12.89}\times{10}^{{-{3}}}{k}{g}\)

(C) \({2.45}\times{10}^{{-{3}}}{k}{g}\)

(D) \({6.45}\times{10}^{{-{3}}}{k}{g}\)

Correct51

The smallest division on main scale of a vernier caplliers is \({1}{m}{m}{\quad\text{and}\quad}{10}\) vernier divisions coincide with \({9}\) main scale divisions. While measuring the length of a line, the zero mark of the vernier scale lies between \({10.2}{c}{m}{\quad\text{and}\quad}{10.3}{c}{m}\) and the third division of vernier scale coincides with a main scale division.

(a) Determine the least count of the callopers.

(b) Find the length of the line.

(a) Determine the least count of the callopers.

(b) Find the length of the line.

Correct6

A vector \(\vec{{A}}\) points vertically upward and \(\vec{{B}}\) points towards north. The vector produce \(\vec{{A}}\times\vec{{B}}\) is

(A) along west

(B) along east

(C) zero

(D) vertically downward

(A) along west

(B) along east

(C) zero

(D) vertically downward

Correct50

A straight rod of length L has one of its end at the origin and the other at \({X}={L}\). If the mass per unit length of the rod is given by \({A}{x}\) where A is constant, where is its centre of mass?

Correct36

Calculate the energy released when 1000 small water drops each of same radius \({10}^{{-{7}}}{m}\) coalesce to form one large drop. The surface tension of water is \({7.0}\times{10}^{{-{2}}}{N}/{m}\).

Correct34

A non-relativistic proton beam passes without deviation through a region of space where there are uniform transverse mutually perpendicular electric and magnetic fields with \({E}={120}{k}{V}{m}^{{-{{1}}}}{\quad\text{and}\quad}{B}={50}{m}{T}.\) Then the beam strikes a grounded target. Find the force which the beam acts on the target if the beam current is equal to \({i}={0.8}{m}{A}\).

Mass of protons \(={1.67}\times{10}^{{-{27}}}{k}{g}\).

Mass of protons \(={1.67}\times{10}^{{-{27}}}{k}{g}\).

Correct40

Is it necessary for a transmitting antenna to be at the same height asthat of the receiving antanna for line of sight communication? A TV transmitting antenna is 81 m tall. How much service area can it cover, if the receiving antena is at the ground level?

Correct38

The intensity of light pulse travelling in an optical fiber decreases according to the relation \({I}={I}_{{{0}}}{e}^{{-\alpha{x}}}\) . The intensity of light is reduced to \({20}\%\) of its initial value after a distance x equal to

(A) In\({\left(\frac{{{1}}}{{\alpha}}\right)}\)

(B) In\({\left(\alpha\right)}\)

(C) \(\frac{{{\left(\text{In}{5}\right)}}}{{\alpha}}\)

(D) In \({\left(\frac{{{5}}}{{\alpha}}\right)}\)

(A) In\({\left(\frac{{{1}}}{{\alpha}}\right)}\)

(B) In\({\left(\alpha\right)}\)

(C) \(\frac{{{\left(\text{In}{5}\right)}}}{{\alpha}}\)

(D) In \({\left(\frac{{{5}}}{{\alpha}}\right)}\)

Correct39

A stone , when thrown on a glass window smashes the window pane to pieces , but a bullet from the gun passes through making a clean hole . Way ?

Correct26

A heavy box of mass 20 kg is placed on a horizontal surface . If coefficient of kinetic friction between the box and the horizontal surface . Is 0.25 calculate the force of kinetic friction Also calculate acceleration produced under a force of 98 N applied horizontally ?

Correct24

Calculate the power of an engine , which can just pull a train of mass 5000 quintals up an incline of 1 in 50 at the rate of \({54}{k}{m}/{h}\) . The resistance due to friction is\({0.8}{N}/\text{quintal}\). Take \({g}={9.8}{m}/{s}^{{{2}}}\) .

Correct22

A vehicles of mass 10 quintals climba up a hill 200m high and thenmoves on a level road with a velocity of \({36}{k}{m}/{h}\) .Calculate its total mechanical energy while running on the top of the hill.

Correct43

A constant power P is applied on a particle of mass m. find kintic energy, velocity and displacement of particle as function of time t.

Correct7

Write the dimensional formula of angular momentum. Is it scale or vector ?

Correct28

A very small particle rests on the top of a hemisphere of radius \({20}{c}{m}\). Calculate the smallest horizontal velocity to be given to it if it is to leave the hemisphere without sliding down its surface, take \({g}={9.8}{m}/{s}^{{{2}}}\).

Correct41

A cylinder of radius \({R}\) and mass \({M}\) rolls without slipping down a plane inclined at an angle \(\theta\). Coeff. of friction between the cylinder and the plane is \(\mu\). For what maximum inclination \(\theta\), the cylinder rolls without slipping ?

(A) \({{\tan}^{{-{1}}}\mu}\)

(B) \({{\tan}^{{-{1}}}{\left({3}\mu\right)}}\)

(C) \({{\tan}^{{-{1}}}{2}}\mu\)

(D) \({{\tan}^{{-{1}}}.}\frac{{{3}}}{{{2}}}\mu\)

(A) \({{\tan}^{{-{1}}}\mu}\)

(B) \({{\tan}^{{-{1}}}{\left({3}\mu\right)}}\)

(C) \({{\tan}^{{-{1}}}{2}}\mu\)

(D) \({{\tan}^{{-{1}}}.}\frac{{{3}}}{{{2}}}\mu\)

Correct42

A man throws the bricks to a height of 12 m where they reach with a speed of \({12}{m}/{s}\). If he throws the bricks such that they just reach that height, what percentage of energy will be saved? \({\left({g}={9.8}{m}/{s}^{{{2}}}\right)}\)

(A) \({9.5}\%\)

(B) \({19}\%\)

(C) \({38}\%\)

(D) \({76}\%\)

(A) \({9.5}\%\)

(B) \({19}\%\)

(C) \({38}\%\)

(D) \({76}\%\)

Correct45

Two lead spheres of \({20}{c}{m}\) and \({2}{c}{m}\) diametre respectively are planet with centres \({100}{c}{m}\) apart. Calculate the attraction between them, given the radius of the Earth as \({6.37}\times{10}^{{{8}}}{c}{m}\) and its mean density as \({5.53}\times{10}^{{{3}}}{k}{g}{m}^{{-{3}}}\). Speciffic gravity of lead \(={11.5}\). If the lead spheres are replaced by bress sphere of the same radii, would the force of attraction be the same?

Correct20

Where will a body weigh more, \({2}{k}{m}\) above the surface of earth or \({2}{k}{m}\) below the surface of earth ?

Correct29

Calculate the percentage increase in length of a wire of diameter 1 mm stretched by a force of half kilo gram weight. Young's modulus of elasticity of wire is \({12}\times{10}^{{{11}}}{\left.{d}{y}\right.}{n}{e}/{c}{m}^{{{2}}}\)

Correct9