Flag 9 grade science> Two unequal masses Pand Q moving along a ...
question mark

Two unequal masses Pand Q moving along a straight lines are brought to rest by applying equal retarding forces. if P moves twice the time q but goes only {1/3}rd of the distance covered by q before coming to rest , the ratio of their velocity is-

ayush , 7 Years ago
Grade 9
anser 1 Answers
Arun

Last Activity: 7 Years ago

Dear Ayush
 

Let the retarding force be F.

Suppose A having mass ‘m’ was initially moving with velocity ‘u’. It comes to rest in time ‘t’ after traveling a distance ‘x’.

Retardation of this mass is, a = F/m

And B having mass ‘M’ was initially moving with velocity ‘U’. It comes to rest in time ‘T’ after traveling a distance ‘X’.

Retardation of this mass is, A = F/M

A/Q,

t = 2T

x = X/3

Also,

F = ma = MA

For A,

0 = u – at

=> a = u/t

Similarly,

A = U/T

So,

a/A = uT/(Ut)

=> a/A = uT/(U × 2T)

=> a/A = u/(2U) ……………….(1)

Again for A,

02 = u2 – 2ax

=> a = u2/(2x)

Similarly,

A = U2/(2X)

So,

a/A = [u2/(2x)]/[U2/(2X)]

=> a/A = (u2/U2)(X/x)

=> a/A = (u2/U2)[X/(X/3)]

=> a/A = 3(u2/U2) ………………(2)

(1) and (2) => u/(2U) = 3(u2/U2)

=> ½ = 3 u/U

=> u/U = 1/6

Thus, ratio of initial velocity of A to initial velocity of B is = 1 : 6

 

Regards

Arun (askIITians forum expert)

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments