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A rocket accelerates straight up by ejecting gas downwards. In a small time interval ∆t, it ejects a gas of mass ∆m at a relative speed u. Calculate KE of the entire system at t + ∆t and t and show that the device that ejects gas does work = `(1/2)∆m u^2` in this time interval (neglect gravity).
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As observed from earth, the sun appears to move in an approximate circular orbit. For the motion of another planet like mercury as observed from earth, this would ______.
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Different points in earth are at slightly different distances from the sun and hence experience different forces due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the c.m. (centre of mass) causing translation and a net torque at the c.m. causing rotation around an axis through the c.m. For the earth-sun system (approximating the earth as a uniform density sphere).
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Particles of masses 2M, m and M are respectively at points A, B and C with AB = ½ (BC). m is much-much smaller than M and at time t = 0, they are all at rest (Figure). At subsequent times before any collision takes place ______.

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If the law of gravitation, instead of being inverse-square law, becomes an inverse-cube law- ______.
- planets will not have elliptic orbits.
- circular orbits of planets is not possible.
- projectile motion of a stone thrown by hand on the surface of the earth will be approximately parabolic.
- there will be no gravitational force inside a spherical shell of uniform density.
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Molecules in air in the atmosphere are attracted by gravitational force of the earth. Explain why all of them do not fall into the earth just like an apple falling from a tree.
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How is the gravitational force between two point masses affected when they are dipped in water keeping the separation between them the same?
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We can shield a charge from electric fields by putting it inside a hollow conductor. Can we shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?
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The gravitational force between a hollow spherical shell (of radius R and uniform density) and a point mass is F. Show the nature of F vs r graph where r is the distance of the point from the centre of the hollow spherical shell of uniform density.
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The gravitational force between a hollow spherical shell (of radius R and uniform density) and a point mass is F. Show the nature of F vs r graph where r is the distance of the point from the centre of the hollow spherical shell of uniform density.
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Shown are several curves (Figure). Explain with reason, which ones amongst them can be possible trajectories traced by a projectile (neglect air friction).
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Six point masses of mass m each are at the vertices of a regular hexagon of side l. Calculate the force on any of the masses.
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Modulus of rigidity of ideal liquids is ______.
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Modulus of rigidity of ideal liquids is ______.
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The maximum load a wire can withstand without breaking, when its length is reduced to half of its original length, will ______.
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A spring is stretched by applying a load to its free end. The strain produced in the spring is ______.
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A mild steel wire of length 2L and cross-sectional area A is stretched, well within elastic limit, horizontally between two pillars (Figure). A mass m is suspended from the mid point of the wire. Strain in the wire is ______.

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A rectangular frame is to be suspended symmetrically by two strings of equal length on two supports (Figure). It can be done in one of the following three ways;
| (a) | ![]() |
| (b) | ![]() |
| (c) | ![]() |
The tension in the strings will be ______.
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Consider two cylindrical rods of identical dimensions, one of rubber and the other of steel. Both the rods are fixed rigidly at one end to the roof. A mass M is attached to each of the free ends at the centre of the rods.
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