Which of the following statements is correct?
(a) Centre of the mass of a body always coincides with the centre of gravity of the body.
(b) Centre of the mass of a body is the point at which the total gravitational torque on the body is zero
(c) A couple on a body produce both translational and rotational motion in a body.
(d) Mechanical advantage greater than one means that small effort can be used to lift a large load.
(b) and (d)
(a) and (b)
(b) and (c)
(b) and (c)
A.
(b) and (d)
Centre of mass may or may not coincide with centre of gravity.
A rocket is intended to leave the Earth's gravitational field. The fuel in its main engine is a little less than the amount that is necessary and an auxiliary engine, (only capable of operating for a short time) has to be used as well. When is it best to switch on the auxiliary engine?
at take-off
When the rocket has nearly stopped with respect to the Earth
It doesn't matter
Can't say
A.
at take-off
The rocket has to reach the highest possible total energy. If the zero level of gravitational potential energy is infinitely far away, then the energy of the rocket standing on the surface on the earth is negative. The energy released during the operation of the engines increases the total energy of the rocket, and the rocket can leave the earth's gravitational field if the sum of its potential and kinetic energies becomes positive.
The energy released in the course of the operation of the principal and auxiliary engines increase the total energy of the rocket and its ejected combustion products by a fixed value; this increase is independent of the moment when the engines are scratched on. However, the speed at which the combustion products fall back to the earth does depend on the timing of the rocket's operations. Indeed, if the auxiliary engine starts working when the rocket is at a greater height, the combustion fall further and their speed and total energy are higher when they hit the ground. This means that the sooner the auxiliary engine is switched on. the higher, the energy ultimately acquired by the rocket. The same concept is valid for the principal engine, and if the only energy consideration applies, it is best to operate the engines for the shortest time and at the highest thrust.
Two 20 g flatworms climb over a very thin wall, 10 cm high. One of the worms is 20 cm long, the other is wider and only 10 cm long. which of the following statement is correct regarding them?
20 cm worm has done more work against gravity
10 cm worm has done more work against gravity
Both worms have done equal work against gravity
Ratio of work done by both the worms is 4:5
B.
10 cm worm has done more work against gravity
The work done against gravity can be calculated from the increased in height of the centre of mass. The centre of mass of a worm folded in two is located at the middle of either half, i.e., at a point one-quarter of the worm's total length from one end.
Thus, the centre of mass of the narrow flat worm travels 5 cm up the wall; while that of the broad worm moves 7.5 cm. Hence, work done by 10 cm worm is more against gravity. Also, the ratio of the work done is 2:3.
If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct?
Raindrops will fall faster
Walking on the ground would become more difficult
'g' on the Earth will not change
Time period of a simple pendulum on the Earth would decrease
C.
'g' on the Earth will not change
If universal gravitational constant becomes tem times then G' = 10 G
Acceleration due to gravity,
So, Acceleration due to gravity increases.
Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will:
Keep floating at the same distance between them
Move towards each other
Move away from each other
Move away from each other
B.
Move towards each other
Both the astronauts are in the condition of weightness. Gravitational force between them pulls towards each other
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