Does the escape speed of a body from the earth depend on
(a) the mass of the body,
(b) the location from where it is projected,
(c) the direction of projection,
(d) the height of the location from where the body is launched?
Choose the correct alternative : (a) Acceleration due to gravity increases/decreases with increasing altitude.(b) Acceleration due to gravity increases/decreases with increasing depth (assume the earth to be a sphere of uniform density).(c) Acceleration due to gravity is independent of mass of the earth/mass of the body.(d) The formula –G Mm \(\frac{1}{r_2 }– \frac{1}{r_1}\) is more/less accurate than the formula mg(r2 – r1) for the difference of potential energy between two points r2 and r1 distance away from the centre of the earth.
The position of a particle is given by r = 3.0t i -2.0t2 j + 4.0 k m. where t is in seconds and the coefficients have the proper units for r to be in metres.(a) Find the v and a of the particle?
(b) What is the magnitude and direction of velocity of the particle at t = 2.0 s ?
State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:
(a) adding any two scalars,
(b) adding a scalar to a vector of the same dimensions,
(c) multiplying any vector by any scalar,
(d) multiplying any two scalars,
(e) adding any two vectors,
(f) adding a component of a vector to the same vector