Question

a certain force gives an object of mass m1 and acceleration of 12 m/s^2 and an object of mass m2 an acceleration would the force give to an object of mass m2 - m1?

Answer 1

Correct Question

A force acts on two objects M and m to produce an acceleration 12 m/s² and 10 m/s² respectively. Find the ratio of the accelerations given by the force to the object of mass M + m and M - m

Solution

The applied force is equal in magnitude

We know that,

$\sf F = Ma$

Thus,

$\sf F = 12M ----------(1) \\ \\ \sf F = 10m ---------(2)$

Dividing equations (1) and (2),we write :

$\sf 12M = 10m \\ \\ \longrightarrow \sf 6M = 5m \\ \\ \longrightarrow \boxed{\sf \dfrac{m}{M} = \dfrac{6}{5} }$

When the system of masses is M + m,

$\sf F = (M + m)a_1 \\ \\ \sf a_1 = \dfrac{F}{M + m} -----------(3)$

When the system of masses is M - m,

$\sf F = (M - m)a_2 \\ \\ \sf a_2 = \dfrac{F}{M - m} ------------(4)$

Dividing equations (3) and (4),we write :

$\boxed{\sf \dfrac{a_1}{a_2} = \dfrac{M - m}{M + m} }$

Dividing numerator and denominator on RHS by M,we will be left with ratio m/M which 6/5

Thus,

$\sf \dfrac{a_1}{a_2} = \dfrac{1 - \dfrac{6}{5}}{1 + \dfrac{6}{5}} \\ \\ \longrightarrow \boxed{\boxed{\green{\sf a_1 : a_2 = - 1 : 11 }}}$