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Two bodies have masses in the ratio 3:1. They experience forces which impart to them acceleration in the ratio 2:9 respectively. Find the ratio of forces the masses experienced.
1 : 4
2 : 1
2 : 3
2 : 5
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Tow bodies A&B=3:2 & 1:9
USING ISAAC NEWTON'S SECOND LAW OF MOTION: {F=M x A}
forces for the two bodies=3x2 : 1x9
A=6 & B=9
DIVIding through with 3(that is the lowest possible integers)
A&B=2:3 ans{c}
Deducing d mathematical representation of Newton's 2nd law of motion,we have F=MA.Frm our quesn
M1=2,A1=3,M2=9,A2=1
Relate them 2gether:
2*3:9*1
=6:9(divide through using their possible smallest integers i.e3 ofcourse)
=2:3 ans.....c
Was asked to post my solution here. Well, here it is:
Consider the two bodies as A and B with A having properties (according to the ratios given) as mass 3 units and acceleration 2 units and B with mass 1 unit and acceleration 9 units.
We all know Isaac Newton's second law of motion which results into the following equation:
Force [F] = Mass [M] x Acceleration [A]
Therefore the forces for the two bodies are thus: Force of A = 3 x 2 = 6 units, and
B = 1 x 9 = 9 units.
Expressing both A and B as ratios would yield a force ratio of 6:9.
Reducing both to the lowest integers possible by dividing through by 3 would give us the ratio of forces as
2:3
This is the final answer, option [C]
But seriously, this is basic stuff! Expected something harder!
Anoda method is,2:1and3:9=3/2*1/9,cross divide,which is 9 divided 3, u get 3,and 2 divided 1 u get 2,which is 2:3,as answer.
we know that force is ;
F=ma
3:1 this is the ratio of their masses
2:9 this is the ratio of their acceleration
recall that:
F=ma
ratio of their forces :
3×2:1×9
6:9
2:3 ans.
can any of you guys (well capable enough)help us who are lost? message me here and I'll reply please.....
we know that f=ma and we are having 2 masses and 2 accelerarions....xo we jst say f1 * m1 = f2 * m2 which is equal "6=9"...then divide both sides with 3 den we have 2:3
Usin force=mass *acceleration,F1=m1*a1=3*2=6units,F2=M2*a2=9*1,nd d forces r in d ratio 6:9,takin it to its lowest term =6/9=2/3 den to its ratio form =2:3
Generally:
F=ma
so therefore-F1=m1a1 and F2=m2a2
Ratios of F1 to F2:
F1/F2=m1a1/m2a2=m1/m2 * a1/a2
F1:F2=3/1 * 2/9
F1:F3=2:3....(ratios does not have unit)
We know that force and acceleration are directly proportional to each other according to Newton's second law of motion, F = ma, where F is the force, m is the mass, and a is the acceleration.
Let the masses of the two bodies be 3x and x (since they are in the ratio of 3:1). Let their respective accelerations be 2a and 9a (since they are in the ratio of 2:9).
According to Newton's second law, the forces experienced by the two bodies can be expressed as:
F1 = m1a1 = (3x)(2a) = 6ax
F2 = m2a2 = (x)(9a) = 9ax
Therefore, the ratio of forces experienced by the two bodies is:
F1 : F2 = 6ax : 9ax = 2 : 3
So the ratio of forces experienced by the two bodies is 2:3.
Using Newton 2nd law:F=ma
m1=3,m2=1,a1=2,a2=9
The above implies:
3*2=1*9
= 6:9
dividing with their smallest integer which is 3,
we ve 2:3(final answer)