Question

Two bodies of masses 'm' and '2m' are acted upon by the same force 'f' . The ratio of acceleration produced in them is ​

Answer 1

Given :

▪ Mass of body A = m

▪ Mass of body B = 2m

▪ Both are acted upon by the same force.

To Find :

▪ Ratio of acceleration produced in them.

Concept :

→ This question is completely based on the concept of Newton's second law of motion.

→ According to Newton's second law,

Applied Force = Rate of change of linear momentum

$\bigstar\:\underline{\boxed{\bf{\red{F=\dfrac{dp}{dt}=ma}}}}$

• F denotes applied force
• dp denotes change in momentum
• dt denotes time interval
• m denotes mass
• a denotes acceleration

Calculation :

$\dashrightarrow\sf\:F_A=F_B\\ \\ \dashrightarrow\sf\:m_Aa_A=m_Ba_B\\ \\ \dashrightarrow\sf\:ma_A=(2m)a_B\\ \\ \dashrightarrow\sf\:a_A=2a_B\\ \\ \dashrightarrow\underline{\boxed{\bf{\green{a_A:a_B=2:1}}}}\:\orange{\bigstar}$