2018-10-01_Physics_For_You

21. Water stands at a depth H in a tank whose side
    walls are vertical as shown in the gure. A hole is
    made on one side of the walls at a depth h below
    the water surface.

h

H–h

v

H

s

(a) At what distance s from the foot of the wall
does the emerging stream of water strike the
oor?
(b) For what value of h this range is maximum?

22. (i) e breaking stress for aluminium is
    7.5 × 10^7 N m–2. Find the greatest length
    of aluminium wire that can hang vertically
    without breaking under its own weight.
    Density of aluminium is 2.7 × 10^3 kg m–3.
    (ii) e shear modulus of a material is always
    considerably smaller than the Young's
    modulus for it. What does it signify?


23. A solid sphere of mass m = 2 kg and density of
    0.5 × 10^3 kg m–3 is held stationary relative to a
    tank lled with water as shown in gure. e tank
    is accelerating vertically upward with acceleration
    2 m s–2.
    (i) Calculate the tension in
    the thread connecting the
    sphere and the bottom of
    the tank.
    (ii) If the thread snaps, calculate
    the acceleration of the sphere with respect to
    the tank. (Density of water is ρ = 1000 kg m–3
    and g = 10 m s–2.)


24. (a) Explain why should the beams used in the
    construction of bridges have large depth and
    small breadth.
    (b) Why are girders given I shape?
    SECTION D


25. Explain what happens when the load on a metal
    wire suspended from a rigid support is gradually
    increased. Illustrate your answer with a suitable
    stress-strain graph.

OR

(a) Pressure decreases as one ascends the

atmosphere. If the density of air is ρ, what is

the change in pressure dP over a dierential

height dh?

(b) Considering the pressure P to be proportional

to the density, nd the pressure P at a height

h if the pressure on the surface of the earth

is P 0.

(c) If P 0 = 1.013 × 10^5 N m–2, ρ 0 = 1.29 kg m–3 and

g = 9.8 m s–2, at what height will the pressure

drop to (1/10) the value at the surface of the

earth?

(d) is model of the atmosphere works for

relatively small distances. Identify the

underlying assumption that limits the model.

26. A bar of cross-section A is subjected to equal and
    opposite tensile forces at its ends. Consider a plane
    section of the bar whose normal makes an angle q
    with the axis of the bar.
    (i) What is the tensile stress on this plane?
    (ii) What is the shearing stress on this plane?
    (iii) For what value of q is the tensile stress
    maximum?
    (iv) For what value of q is the shearing stress
    maximum?

F q F

OR

State and prove Bernoulli's theorem.

27. A light rod of length 2 m is suspended horizontally
    by means of two vertical wires of equal lengths
    tied to its ends. One of the wires is made of
    steel and is of cross-section A 1 = 0.1 cm^2
    and the other is of brass and is of cross-section
    A 2 = 0.2 cm^2. Find out the position along the rod
    at which a weight must be suspended to produce
    (i) equal stress in both wires, (ii) equal strain in
    both wires. For steel, Y = 20 × 10^10 N m–2 and for
    brass Y = 10 × 10^10 N m–2.
    OR
    Explain how does a body attain a terminal velocity
    when it is dropped from rest in a viscous medium.
    Derive an expression for the terminal velocity of
    a small spherical body falling through a viscous
    medium.