Mechanics | Relativity Answers

The force of resistance on an object moving through a fluid is proportional to the
square of its velocity. The initial velocity of an object of mass 1 kg moving through the
fluid is 40 ms−1. After 5 s the velocity reduces to 20 ms−1. Calculate its velocity after
10 s

In an experiment to discover the acceleration due to gravity, a rock was dropped on the planet Zeus.
If it fell a distance of 15 m in 5 s, the acceleration of gravity on Zeus is

The density of a ball is (300 ± 8) kg m -3 .
The ball is placed on a metre rule to find its diameter.
One end of a diameter is opposite the 35 cm mark and the other end is at 78 cm and the error in each of these measurements is
± 1 cm.
Find the mass of the ball

A spring is stretched 5 ×10 m
−2
by a force of .N 5×10−4
A mass of 0.01 kg is placed
on the lower end of the spring. After equilibrium has been reached, the upper end of the
spring is moved up and down so that the external force acting on the mass is given by
F(t) = 20 cos ωt. Calculate (i) the position of the mass at any time, measured form the
equilibrium position and (ii) the angular frequency for which resonance occurs.

To find the optimum shape for a cross-section of a beam against bending, beam sections of a square, circle and equilateral triangle with the same cross-sectional area (A) are considered. If the beams have the same length (L), Young’s Modulus (E) and support condition, determine which shape of the beam is the best against bending

7. A box is pulled straight across the floor at a constant speed. It is pulled with a horizontal force of 48 N.
a. Find the net force (in N) on the box.
b. Find the force of friction (in N) from the floor on the box.
c. The person pulling on the box stops pulling and the box comes to a rest. Find the force of friction (in N) on the box when at rest.

A man standing on the ground wants to climb to the top of a vertical pole 13meters tall.He climbs 5meters in 1second and then slips downwards 3meters in the next second.He gains climb 5meters in 1 second and slip by 3meters in the next second,and so on.Draw the x-1 graph of the motion of the man and hence find the time it will take the man to reach the top of the pole

If vector A=Axi+Ayj+Azk,
B=Bxi+Byj+Bzk and
C=Cxi+Cyj+Czk
Show that the scalar triple product of the vector is[Ax Ay Az][Bx By Bz ][Cx Cy Cz]
Note:the bracket above is a 3 by 3 matrix

. The equation of a stationary wave on a string fixed at both ends is given by
y( x,t) = 2sin πx cos100πt
where x and y are measured in metre and t in second. Calculate the amplitude,
wavelength and frequency of component waves whose superposition generated this
stationary wave. Also write the equations of component waves.

A man pushes a box of 40 kg up incline plane of 15°, if the man applies a horizontal force 200N and the box moves up the plane a distance of 20 m at a constant velocity and the coefficient of friction is 0.1, find
1)The work done by the man
2)And also find the work done against friction