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Suppose you are told that the linear size of everything in the universe has been doubled overnight. Can you test this statement by measuring sizes with a metre stick? Can you test it by using the fact that the speed of light is a universal constant and has not changed? What will happen if all the clocks in the universe also start running at half the speed?
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Suggest a way to measure the distance between the sun and the moon.
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Find the dimensions of electric dipole moment p .
The defining equations are p = q.d and M = IA;
where d is distance, A is area, q is charge and I is current.
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Find the dimensions of magnetic dipole moment M.
The defining equations are p = q.d and M = IA;
where d is distance, A is area, q is charge and I is current.
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Express the power of a 100 watt bulb in CGS unit.
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The kinetic energy K of a rotating body depends on its moment of inertia I and its angular speedω. Assuming the relation to be \[k = KI^0w^B\] where k is a dimensionless constant, find a and b. Moment of inertia of a sphere about its diameter is \[\frac{2}{5}M r^2\]
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The velocity of a particle is towards west at an instant. Its acceleration is not towards west, not towards east, not towards north and towards south. Give an example of this type of motion .
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At which point on its path a projectile has the smallest speed?
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A particle moves on a given straight line with a constant speed ν. At a certain time it is at a point P on its straight line path. O is a fixed point. Show that \[\vec{OP} \times \vec{\nu}\] is independent of the position P.
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The force on a charged particle due to electric and magnetic fields is given by \[\vec{F} = q \vec{E} + q \vec{\nu} \times \vec{B}\].
Suppose \[\vec{E}\] is along the X-axis and \[\vec{B}\] along the Y-axis. In what direction and with what minimum speed ν should a positively charged particle be sent so that the net force on it is zero?
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In a projectile motion the velocity
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Two bullets are fired simultaneously, horizontally and with different speeds from the same place. Which bullet will hit he ground first?
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The electric current in a discharging R−C circuit is given by i = i0 e−t/RC where i0, R and C are constant parameters and t is time. Let i0 = 2⋅00 A, R = 6⋅00 × 105 Ω and C = 0⋅500 μF. (a) Find the current at t = 0⋅3 s. (b) Find the rate of change of current at at 0⋅3 s. (c) Find approximately the current at t = 0⋅31 s.
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Find the area bounded under the curve y = 3x2 + 6x + 7 and the X-axis with the ordinates at x = 5 and x = 10.
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Find the area enclosed by the curve y = sin x and the X-axis between x = 0 and x = π.
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Find the area bounded by the curve y = e−x, the X-axis and the Y-axis.
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A rod of length L is placed along the X-axis between x = 0 and x = L. The linear density (mass/length) ρ of the rod varies with the distance x from the origin as ρ = a + bx. (a) Find the SI units of a and b. (b) Find the mass of the rod in terms of a, b and L.
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A metre scale is graduated at every millimetre. How many significant digits will be there in a length measurement with this scale?
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A person travelling at 43.2 km/h applies the brake giving a deceleration of 6.0 m/s2 to his scooter. How far will it travel before stopping?
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A train starts from rest and moves with a constant acceleration of 2.0 m/s2 for half a minute. The brakes are then applied and the train comes to rest in one minute. Find the total distance moved by the train.
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