Answer Happy

The maximum height of a mountain on earth is
limited by the rock flowing under the enormous
weight above it. Studies show that maximum
height depends on young’s modulus (Y) of the
rod, acceleration due to gravity (g) and the density
of the rock (d).
(a) Write an equation showing the dependence
of maximum height (h) of mountain on Y, g
and d. It is given that unit of Y is Nm–2.
(b) Take d = 3 × 103
kg m–3, Y = 1 × 1010 Nm–2
and g = 10 ms–2 and assume that maximum
height of a mountain on the surface of earth
is limited to 10 km [height of mount Everest
is nearly 8 km]. Write the formula for h.
A particle of mass m is given an initial speed V0. It
experiences a retarding force that is proportional
to the speed of the particle (F = aV). a is a
constant.
(a) Write the dimensional formula of constant a.
(b) Using dimensional analysis, derive a formula
for stopping time (t) of the particle. Does
your formula tell you how ‘t’ depends on
initial speed V0? What can you predict about
the constant obtained in the formula?