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Three blocks with masses `m, 2m and 3m` are connected by strings, as shown in the figure. After an upward force `F` is applied on block `m`, the masses move upward at constant speed `v`. What is the net force on the block of mass `2m`? (Take, g is the acceleration due to
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A box of mass `2 kg` is placed on the roof of a car. The box would remain stationary until the car attains a maximum acceleration. Coefficient of static friction between the box and the roof of the car is `0.2 and g = 10 ms^(-2)`. The maximum acceleration of the car, for the box to remain stationary,
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A car is moving in a circular horizontal track of radius 10.0 m with a constant speed of `10.0 ms^(-1)`. A plumb bob is suspended from the roof of the car by a light rigid rod of length 10.0 m. The angle made by the rod with the track is (Take,`g = 9.8
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If radius of earth is reduced to half without changing its mass, then match the following columns and choose the correct option from the codes given below. Column I Column II A. Angular momentum of earth p. Will become one fourth B. Time period of rotation of earth q. Will become four times C. Rotational kinetic energy of earth r. No change
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Centre of Mass The centre of mass of a body or a system of bodies is the point which moves as though all of the mass were concentrated there and all external forces were applied to it. Hence, a point at which the entire mass of the body or system of bodies is supposed to be concentrated is known as the centre of mass. If a system consists of more than one particles (or bodies) and net external force on the system in a particular direction is zero with centre of mass at rest. Then, the centre of mass will
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Moment of InertiaA heavy wheel called flywheel is attached to the shaft of steam engine, automobile engine etc., because of its large moment of inertia, the flywheel opposes the sudden increase or decrease of the speed of the vehicle. It allows a gradual change in the speed and prevents jerky motion and hence ensure smooth ride of passengers.Moment of inertia of a rod of mass `m` and length `l` about its one end is `I`. If one-fourth of its length is cut away, then moment of inertia of the remaining rod about its one end will
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The mass of the earth is `6.00 xx 10^(24) kg` and that of the moon is `7.40 xx 10^(22) kg`. The constant of gravitation `G=6.67 xx 10^(-11) N-m^2kg^(-2)`. The potential energy of the system is `- 7.79 xx 10^(28)J`.The mean distance between the earth and the moon
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A satellite of mass m revolving with a velocity v around the earth. With reference to the above situation, match the Column I (types of energy) with Column II (expression) and select the correct answer from the codes given below. Column I Column II A. Kinetic energy of the satellite p. `-1/2mv^2` B. Potential energy of the satellite q. `1/2mv^2` C. Total energy of the satellite r. `-mv^2`
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Earth’s SatelliteEarth satellites are objects which revolve around the earth. Their motion is very similar to the motion of planets around the Sun. In particular, their orbits around the earth are circular or elliptic. Moon is the only natural satellite of the earth with a near circular orbit with a time period of approximately 27.3 days which is also roughly equal to the rotational period of the moon about its own axis. Also, the speed that a satellite needs to be travelling to break free of a planet or moon’s gravity well and leave it without further propulsion is known
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A spring is cut into two equal halves. How is the spring constant of each half
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In a horizontal pipeline of uniform area of cross – section, the pressure falls by `5 N`/`m^2` between two points separated by a distance of 1 Km. What is the change in kinetic energy per Kg of oil flowing at these points? Given Density of oil = 800
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The ends of the two rods of different materials with their thermal conductivities, radii of cross – section and length in the ratio 1:2 are maintained at the same temperature difference. If the rate of flow of heat through the larger rod is 4 cal |s, what is the rate of flow through the shorter
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A metre long narrow bore held horizontally (and closed at one end) contains a 76 cm long mercury thread, which traps a 15 cm column of air. What happens if the tube is held vertically with the open end at the bottom
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Which of the following functions of time represent (a) periodic and (b) non-periodic motion? Give the period for each case of periodic motion [ω is any positive constant]. sin ωt + cos
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Which of the following functions of time represent (a) periodic and (b) non-periodic motion? Give the period for each case of periodic motion [ω is any positive constant]. log
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Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic
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(a) What is the largest average velocity of blood flow in an artery of radius `2×10^(–3)`m if the flow must remain lanimar? (b) What is the corresponding flow rate ? (Take viscosity of blood to be 2.084 × 10–3 Pa
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Mercury has an angle of contact equal to 140° with soda lime glass. A narrow tube of radius 1.00 mm made of this glass is dipped in a trough containing mercury. By what amount does the mercury dip down in the tube relative to the liquid surface outside ? Surface tension of mercury at the temperature of the experiment is 0.465 N `m^(–1)`. Density of mercury = `13.6 × 10^3` kg
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Choose the correct alternative : (a) Acceleration due to gravity increases/decreases with increasing altitude. (b) Acceleration due to gravity increases/decreases with increasing depth (assume the earth to be a sphere of uniform density). (c) Acceleration due to gravity is independent of mass of the earth/mass of the body. (d) The formula –G Mm(1/`r_2` – 1/`r_1`) is more/less accurate than the formula mg(`r_2 – r_1`) for the difference of potential energy between two points `r_2` and `r_1` distance away from the centre of the
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Two discs of moments of inertia `I_1` and `I_2` about their respective axes (normal to the disc and passing through the centre), and rotating with angular speeds `ω_1` and `ω_2` are brought into contact face to face with their axes of rotation coincident. (a) What is the angular speed of the two-disc system? (b) Show that the kinetic energy of the combined system is less than the sum of the initial kinetic energies of the two discs. How do you account for this loss in energy? Take `ω_1` ≠
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