302 - Mechanics part 1 Questions Answers

I think we have to caculate change in y

since y = sin x

so dy = cosx dx = cosπ/3* π/100 = π/200

the initial velocity of car = 50j      and after turn velocity = -50i                              here i and j are the unit vectors along east and north direction

so change in velocity = -50i - 50j

its mod = 50 √2 = 70

Because in barometer the extra Hg level will experience a downward force so Hg level will decrease.

Take your right hand fingers along A and curl these fingers along B, thumb will give you an idea for A × B. for the given problem answer will be west.

|A+B|² = |A|² + |B|²+ 2A.B            (1) 

|A-B|² = |A|² + |B|² - 2A.B             (2)

on subtracting (2) by (1)

|A+B|² - |A-B|² = 4A.B

so C² = |A-B|² + 4A.B

or C² = |A-B|² +4|A||B|cos120

since cos120 is negative so C will be less than |A-B|  

for the distance upto fermi level order will be N>E>G

but  the distance between electrons is greater than fermi level so the given order is justified because now nuclear forces will be very weak.

by formula s = ut + 1/2 a t²

u = 0 [given]

so       s = 1/2 a (5)²= 25a/2       for first 5 sec.

and    s = 1/2 a (10)² = 50a        for total 10 sec. from start

so for next 5 sec. distance = 50a - 25a/2 = 75a/2

answer :  a'³ = a³ (1+ γ3)     here a' is the side of the cube after heating it

so a' = a (1+3γ)^1/3

so area increment = 6a'² -  6a² = 6a² [(1+3γ)^2/3 - 1] = 6a² [ 2γ] = 12γa²

Please submit all the questions seperately. 

λ = v/n = 300/500 

i think you are asking about increment in speed

so according to formula v'/v  = [(T+2)/T]^1/2 

or v'/v = 1 + (1/T)

so v' - v = v(1/T) = 332*1/273 =  1.22       here 332 is the speed of sound at 273K

when a machine works , you should not count gravity, for example if we raise our hand upword with uniform velocity then gravity makes no problem in it because our hand is working by our internal capabilitites

first calculate distance of 4 seconds by using s = ut + 1/2 a t²

then distance of 4.5 sec. by same formula 

difference of these 2 is the distance of 5th half sec.

but some writter consider 5th half as 1/2 +1/2+1/2+1/2+1/2 means 2.5

so they use the same formula first for 2 sec then for 2.5 sec, then their difference.

according to my opinion first is more true way to solve.

Dear Sarika please submit only one question in a box, for a new question use another box so that i could give answers more quickly.

According to the given condition

x² = 2+t

on differentiaing we get 2x dx/dt = 1

or v = 1/2x

now differentiate it again we get dv/dt = -(1/2x² )(dx/dt) = -(1/2x2 )(-1/2x) = 1/4x³                                  

Yes, I will do very soon.

Since there is no force for accelerating the larger block so larger block will be retarded due to this smaller block will move in forward direction 

for the process equations are 

0 + (µ/2)mg - µ(M+m)g = Ma   (1)

(µ/2)mg - ma = ma₁                 (2)

take the value of a from eq (1) to eq (2) and get a₁

then l = 0t + (1/2)a₁ t²

According to the given diagram       Mg - T = Ma,             T = (M'+m)a       and           macosθ = mgsinθ        

solve these equations.

Dear Amit 

this book is not available here so please send the question. 

Since every heavenly body like sun, earth, moon are rotating freely in free space, there is no body which is placed on a base, so rotation of every body depends on all the surrounding bodies. It means its track will also depend on the attraction forces given by all the surrounding bodies.