Mechanics | Relativity Answers

If a and b are two sides of a parallelogram and c and d are the diagonals then :-
(1) c2 + d2 = a2 + b2
(2) c2 + d2 = 2 (a2 + b2)
(3) c2 – d2 = a2 – b2
(4) c2 – d2 = 2 (a2 – b2)

An experiment includes a wheel with a moment of inertia (I). A mass (M) is connected to a belt and runs over a drum of radius (R). The other end of the belt is attached to a spring of stiffness (K) that is connected to the ground.
Show that if the mass is pulled down with a force (F) and then released, that the system will oscillate with simple harmonic motion with a frequency given by…
F = 1/(2 pi) sqrt(k/(M+i/R^2))

Two masses of 2kg and 4kg are connected by a light string passing over a light frictionless pulley. If the system is released from rest determine the velocity of the 4kg mass when it has descended a distance of 1.4m

I read it in a textbook but didn't get it...
When knife is sharpened by pressing it against a grinding stone, the sparks fly off along the tangent to the grinding stone, on account of direction of inertia.
How the concept of direction of inertia is working here...could you be a little detailed??

The distance between the oxygen molecule and each of the hydrogen atoms in a water
(H2
O) molecule is 0.96 Å and the angle between the twooxygen-hydrogen bonds is
105°. Treating the atoms as particles, find the centre of mass of the system.

if there is a crest at x=3m at time t, find three other positions of the crest at that instant?

Find the position and magnification,m,of the image formed by a concave mirror of focal length 24 cm when an object is placed 40 cm from the mirror given that m is
VU

a. 50cmand24

b. 60cmand24

c. 50cmand15

d. 60cmand15

A 2400 W engine pulls a 200 kg block at constant speed up a 12.0 m long, 25.0° incline.
Determine long does it takes to cover this distance.

A force
F⃗
at an angle of
θ
above the horizontal displaces an object through a distance S in its along the horintal. Which of the following is the CORRECT expression for the work done on the object by the force?
a. F⃗ ⋅s⃗ cosθ
b. F⃗ ×s⃗
c. Fssinθ
d. Fscosθ

A block of wood is placed on an inclined plane. The angle
θ
(where
θ
is non-zero) of the inclined plane is gradually increased until the block is at the verge of sliding down the incline. What is the coefficient of friction between the block and the incline?
a.cosθ
b.tanθ
c.sinθ
d.cotθ