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The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration due to gravity ______.
Concept: undefined >> undefined
Which of the following options are correct?
- Acceleration due to gravity decreases with increasing altitude.
- Acceleration due to gravity increases with increasing depth (assume the earth to be a sphere of uniform density).
- Acceleration due to gravity increases with increasing latitude.
- Acceleration due to gravity is independent of the mass of the earth.
Concept: undefined >> undefined
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The stress-strain graphs for two materials are shown in figure (assume same scale).
![]() Material (i) |
![]() Material (i) |
- Material (ii) is more elastic than material (i) and hence material (ii) is more brittle.
- Material (i) and (ii) have the same elasticity and the same brittleness.
- Material (ii) is elastic over a larger region of strain as compared to (i).
- Material (ii) is more brittle than material (i).
Concept: undefined >> undefined
The stress-strain graphs for two materials are shown in figure (assume same scale).
![]() Material (i) |
![]() Material (i) |
- Material (ii) is more elastic than material (i) and hence material (ii) is more brittle.
- Material (i) and (ii) have the same elasticity and the same brittleness.
- Material (ii) is elastic over a larger region of strain as compared to (i).
- Material (ii) is more brittle than material (i).
Concept: undefined >> undefined
Pressure decreases as one ascends the atmosphere. If the density of air is ρ, what is the change in pressure dp over a differential height dh?
Concept: undefined >> undefined
Considering the pressure p to be proportional to the density, find the pressure p at a height h if the pressure on the surface of the earth is p0.
Concept: undefined >> undefined
A bimetallic strip is made of aluminium and steel (αAl > αsteel) . On heating, the strip will ______.
Concept: undefined >> undefined
A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly ______.
Concept: undefined >> undefined
An aluminium sphere is dipped into water. Which of the following is true?
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As the temperature is increased, the time period of a pendulum ______.
Concept: undefined >> undefined
The radius of a metal sphere at room temperature T is R, and the coefficient of linear expansion of the metal is α. The sphere is heated a little by a temperature ∆T so that its new temperature is T + ∆T. The increase in the volume of the sphere is approximately ______.
Concept: undefined >> undefined
A student records the initial length l, change in temperature ∆T and change in length ∆l of a rod as follows:
| S.No. | l(m) | ∆T (C) | ∆l (m) |
| 1. | 2 | 10 | `4 xx 10^-4` |
| 2. | 1 | 10 | `4 xx 10^-4` |
| 3. | 2 | 20 | `2 xx 10^-4` |
| 4. | 3 | 10 | `6 xx 10^-4` |
If the first observation is correct, what can you say about observations 2, 3 and 4.
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Find out the increase in moment of inertia I of a uniform rod (coefficient of linear expansion α) about its perpendicular bisector when its temperature is slightly increased by ∆T.
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Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of 57°C is drunk. You can take body (tooth) temperature to be 37°C and α = 1.7 × 10–5/°C, bulk modulus for copper = 140 × 109 N/m2.
Concept: undefined >> undefined
A rail track made of steel having length 10 m is clamped on a raillway line at its two ends (figure). On a summer day due to rise in temperature by 20° C, it is deformed as shown in figure. Find x (displacement of the centre) if αsteel = 1.2 × 10–5/°C.

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Show that for a particle executing S.H.M, velocity and displacement have a phase difference of π/2.
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The displacement of an elastic wave is given by the function y = 3 sin ωt + 4 cos ωt. where y is in cm and t is in second. Calculate the resultant amplitude.
Concept: undefined >> undefined
For the harmonic travelling wave y = 2 cos 2π (10t – 0.0080x + 3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of 4 m.
Concept: undefined >> undefined
For the harmonic travelling wave y = 2 cos 2π (10t – 0.0080x + 3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of 0.5 m
Concept: undefined >> undefined
For the harmonic travelling wave y = 2 cos 2π (10t – 0.0080x + 3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of `λ/2`
Concept: undefined >> undefined


