51 - Mechanics Part 2 Questions Answers

According to the given conditions 

in first case block is completely inside water by putting 10 kg in it means density of block will be less than that of water

according to the law of floatation we know that 

wt. of solid = upthrust

so 10g + AL(0.01)Dg = AL(0.01)dg

in second case

AL(0.01)Dg = A[L-2](0.01)dg

substracting 2nd eq. by 1st eq. we will get A = 1/2

now initial lenght in start is not provided by you, if it is given then calculate V = AL(0.01)

In thid question d and D are densities of liquid and solid, A and L are area of bottom of block and its length in cm.   0.01 is for converting cm. into m.

since a cetrifugal force works on the body and this force depends on angular speed so statement is correct.

saturation of V P, because due to this drops will be created.

and surface tension cause for the shape of drop

since inside soap bubble pressure is given by the formula P₀ + 4T/R and on pushing air  R will increase so pressure will decrease.

since inside soap bubble pressure is given by the formula P₀ + 4T/R and on pushing air  R will increase so pressure will decrease.

escape velocity = √(2GM/R)   so 1/2 of escape = 1/2√(2GM/R)

so according to given condition on applying energy conservation we will get 

energy at start = energy at the heighest point

or    -GMm/R +  mv²/2 =  -GMm/R₁ +  0

or     - GMm/R   +  2GMm/8R =  -GMm/R₁ + 0

solve now for finding R₁  then find R₁-R

Formula for gravitational potential at centre is -3/2 GM/R so if R will decrease V will increse numerically but - is present so decreases

when elevator will move in upward direction the extra Hg level will feel a down force and given that in movable condition it is 76 cm. Hg so really it will be more than 76 cm. 

The tidal force is a secondary effect of the force of gravity and is responsible for the tides. It arises because the gravitational force per unit mass exerted on one body by a second body is not constant across its diameter, the side nearest to the second being more attracted by it than the side farther away. Stated differently, the tidal force is a differential force. Consider three things being pulled by the moon: the oceans nearest the moon, the solid earth, and the oceans farthest from the moon. The moon pulls on the solid earth, but it pulls harder on the near oceans, so they approach the moon more causing a high tide; and the moon pulls least of all on the far oceans (on the other side of the planet), so they stay behind more, causing another high tide at the same time. If we imagine looking at the Earth from space, we see that the whole Earth was pulled, but the near oceans more and the far oceans less; the far oceans stayed behind since they are pulled less (since they are farther away).

Tidal effects become particularly pronounced near small bodies of high mass, such as neutron stars or black holes, where they are responsible for the "spaghettification" of infalling matter. Tidal forces create the oceanic tide of Earth's oceans, where the attracting bodies are the Moon and, to a lesser extent, the Sun.

Formula

(axial) 

after making the diagram, complete the miniscus as a sphere, then following conditions will be obtained

1) h = R(1-cosθ)  here h, R and θ are height of miniscus, radius of the sphere and  contact angle.

2) R = r/cosθ, r is the radius of beaker

3) tanθ = g/rw²

4) πr²hρ - πR³ρcos²θ = 2πrTcosθ

There are 4 equations, remove R, θ and T and get a relation between h and r in terms of g, w, ρ and π