Overview

The mass density of a planet of radius $R$  varies with the distance   $r$ from its centre as $\rho \left(r\right)={\rho }_0\left(1-\frac{r^2}{R^2}\right)$   . Then the gravitational field is maximum at:

Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area 0.5 m². It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is : (g = 10 m/s²)

A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg, kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is

In the following, digital circuit, what will be the output at ' Z ', when the input (A, B) are (1,0), (0,0), (1,1), (0,1)

A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius Rₑ. By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become √(3/2) times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is R. Value of R is:

The mass density of a spherical galaxy varies as K/r over a large distance 'r' from its center. In that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on R as:

A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is: