51 - Mechanics Part 2 Questions Answers
A nylon rope 3 cm in diameter has a breaking strength of 1.5 x 105 N. The breaking strength for a similar rope 1.5cm in diameter is
breaking stress will remain same
A cubical block of a metal having shear modulus η is fixed from one face as shown in figure and constant force F is applied on it. Find the shear strain produced in it.
If L is the angular momentum of a satellite revolving around earth is a circular orbit of radius r with speed v, then (i) L α v
(ii) L α r
(iii) L α √v
(iv) L α √r
L = m*v*r
If potential energy of a body of mass m on the surface of earth is taken as zero then its potential energy at height h above the surface of earth is [ R is radius of earth and M is mass of earth]
[-GMm/(R+h)]-[-GMm/R] = GMm[1/R - 1/(R+h)]
solve ?
Two points masses having m and 4m are placed at distance at r. The gravitational potential at a point, where gravitational field intensity zero is
field intensity at distance x from m = Gm/x2 - G4m/(r-x)2
compare it to 0 and find x
then calculate gravitational potential at the point
During motion of a planet from perihelion to aphelion the work done by gravitational force of sun on it is positive or negative.
change in K E = work done by all the forces
and from perihelion to aphelion velocity decreases
so work done will be negative
If an object is projected vertically upwards with speed, half the escape speed of earth , then the maximum height attained by it is [R is radius of earth]
from ground to that point
1/2 m[√(2gR)/2]2 + [-GMm/R] = 0 + [-GMm/(R+h)]
solve for h
Two point masses having mass m and 2m are placed at distance d. The point on the line joining point masses, where gravitational field intensity is zero will be at distance
let the point will be at a distance of x from m then compare the gravitational field of the two masses at that point
If earth suddenly stop rotating, then the weight of an object of mass m at equator will [ ω is angular speed of earth and radius R is its radius]
In rotating condition mass at equator is mg-mRω2
if earth stops rotation then it will become mg so increases by mRω2
Three particles A,B and C each of mass m are lying at the corners of an equilateral triangle of side L. If the particle A is released keeping the particles B and C fixed, the magnitude of instantaneous acceleration of A is
force by the other two on A = Gmm/L2 each but the angle between the two forces is 60 degree so resultant force = √3Gmm/L2
now calculate acceleration?