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A rod of length 1.05 m having negligible mass is supported at its ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths as shown in Fig.. The cross-sectional areas of wires A and B are 1.0 `mm^2` and 2.0 `mm^2` ,respectively. At what point along the rod should a mass m be suspended in order to produce (a) equal stresses and (b) equal strains in both steel and aluminium wires.
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Mar 19, 2022
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As you have learnt in the text, a geostationary satellite orbits the earth at a height of nearly 36,000 km from the surface of the earth. What is the potential due to earth’s gravity at the site of this satellite ? (Take the potential energy at infinity to be zero). Mass of the earth = `6.0×10^(24)` kg, radius = 6400
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Mar 19, 2022
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A metal bar 70 cm long and 4.00 kg in mass supported on two knife-edges placed 10 cm from each end. A 6.00 kg load is suspended at 30 cm from one end. Find the reactions at the knifeedges.(Assume the bar to be of uniform cross section and
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Two particles, each of mass m and speed v, travel in opposite directions along parallel lines separated by a distance d. Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is
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marks3
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To maintain a rotor at a uniform angular speed of 200 rad `s^(-1)`, an engine needs to transmit a torque of 180 N m. What is the power required by the engine ? (Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional torque). Assume that the engine is 100%
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A solid cylinder rolls up an inclined plane of angle of inclination 30°. At the bottom of the inclined plane the centre of mass of the cylinder has a speed of 5 m/s. (a) How far will the cylinder go up the plane? (b) How long will it take to return to the
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A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination 30°. The coefficient of static friction `µ_s` = 0.25. (a) How much is the force of friction acting on the cylinder ? (b) What is the work done against friction during rolling ? (c) If the inclination θ of the plane is increased, at what value of θ does the cylinder begin to skid, and not roll perfectly
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Displacement versus time curve for a particle executing S.H.M. is shown in Fig. . Identify the points marked at which velocity of the oscillator is
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A body of mass m is attached to one end of a massless spring which is suspended vertically from a fixed point. The mass is held in hand so that the spring is neither stretched nor compressed. Suddenly the support of the hand is removed. The lowest position attained by the mass during oscillation is 4cm below the point, where it was held in hand.
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Calculate the angle of 10
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A man wishes to estimate the distance of a nearby tower from him. He stands at a point A in front of the tower C and spots a very distant object O in line with AC. He then walks perpendicular to AC up to B, a distance of 100 m, and looks at O and C again. Since O is very distant, the direction BO is practically the same as AO; but he finds the line of sight of C shifted from the original line of sight by an angle θ= 400 (θ is known as ‘parallax’) estimate the distance
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The period of oscillation of a simple pendulum is `T. = 2π sqrt(L/G)` Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. What is the accuracy in the determination of g
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Each side of a cube is measured to be 7.203 m. What are the total surface area and the volume of the cube to appropriate significant
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The force acting on an object of mass m traveling at velocity υ in a circle of radius r is giving by `F=(mv^2)/r` The measurements recorded as m `m= 3.5kg +-0.1``υ = 20 m'/'s +-1 m'/'s``' '` `r=12.5m+- 0.5 m` Find the maximum possible (1) fractional error (2) % error in the measurement of force. How will you record the
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What is the difference between `A^o` and
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A radar signal is beamed towards a planet from the earth and its echo is received seven minutes later. Calculate the velocity of the signal, if the distance between the planet and the earth is
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chapter2
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A function f (θ ) is defined as: `f(θ)=1- θ+θ^2/(2!)-θ^3/(3!)+θ^4/(4!)........` Why is it necessary for q to be a dimensionless
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Moon is seen to be of `(1⁄2)^°` diameter from the earth. What must be the relative size compared to the
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A new system of units is proposed in which unit of mass is α kg, unit of length β m and unit of time γ s. How much will 5 J measure in this new
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Match the Column I (domains) with Column II (relation) and select the correct option from the codes given below. Column I Column II A. Mechanics P. electric and magnetic fields B. Electrodynamics q. macroscopic equilibrium C. Thermodynamics r. Newton’s laws of motion
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