A constant force acts on two different masses independently producing accelerations a1 and a2. When the same force acts on their combined mass, the acceleration produced is

Question

A constant force acts on two different masses independently producing accelerations a1 and a2. When the same force acts on their combined mass, the acceleration produced is (A) a1 +a2  (B) a1a2  (C) (a1a2/a1 +a2) (D) √a12 +a22

Tardigrade Admin · Accepted Answer

Here, F = m1a1 or , m1 = (F/a1) F = m2a2 or, m2 = (F/a2) F = (m1 +m2)a or, a =(F/(m1+m2)) or, a = (F/(F / a1)+(F / a2)) = (a1a2/a1 +a2)

Q. A constant force acts on two different masses independently producing accelerations $a_{1}$ and $a_{2}$ . When the same force acts on their combined mass, the acceleration produced is

$a_{1} + a_{2}$

$a_{1} a_{2}$

$\frac{a _{1} a _{2}}{a _{1} + a _{2}}$

$a_{1}^{2} + a_{2}^{2}$

Here, $F = m_{1} a_{1} or, m_{1} = \frac{F}{a _{1}}$
$F = m_{2} a_{2} or, m_{2} = \frac{F}{a _{2}}$
$F = (m_{1} + m_{2}) a$
$or, a = \frac{F}{( m _{1} + m _{2} )}$
$or, a = \frac{F}{( F / a _{1} ) + ( F / a _{2} )} = \frac{a _{1} a _{2}}{a _{1} + a _{2}}$

Q. A constant force acts on two different masses independently producing accelerations a1​ and a2​. When the same force acts on their combined mass, the acceleration produced is

a1​+a2​

a1​a2​

a1​+a2​a1​a2​​

a12​+a22​​