The sun is less bright at morning and evening as compared to at noon although its distance from the observer is almost the same. Why ?

If Earth be at one fourth its present distance from the Sun, how many days will there be in a year?

Positive charge Q is distributed uniformly over a circular ring of radius R. A particle having a mass m and a negative charge q, is placed on its axis at a distance x from the centre. Find the force on the particle. Assuming x is very less than R, find the time period of oscillation of the particle if it is released from there.

Statement 1 : If aa n db are real numbers and c >0, then the locus represented by the equation |a y-b x|=csqrt((x-a)^2+(y-b)^2) is an ellipse. Statement 2 : An ellipse is the locus of a point which moves in a plane such that the ratio of its distances from a fixed point (i.e., focus) to that from the fixed line (i.e., directrix) is constant and less than 1.

Two satellite A and B of the same mass are revolving around the Earth in circular orbits such that the distance of B from the centre of the Earth is thrice as compared to the distance of A from the centre. What will be the ratio of centripetal force on B to that on A.

What can be said about the centre of mass of a uniform hemisphere without making any calculation? Will its distance from the centre be more than r/2 or less than r/2?

Statement 1 : A bullet is fired and it hits a target. An observer in the same plane heard two sounds: the crack of the rifle and the thud of the bullet striking the target at the same instant. Then the locus of the observer is a hyperbola where the velocity of sound is smaller than the velocity of the bullet. Statement 2 : If the difference of distances of a point P from two fixed points is constant and less than the distance between the fixed points, then the locus of P is a hyperbola.