Question

A force acting on a body of mass 7 kg produces an acceleration of 10 ms−2. The acceleration that the same force will produce in a body of mass 9 kg will be:

Answer 1

Answer:

$\bf 7.\overline{7}$ m/s²

Explanation:

As per the provided information in the given question, we have :

• A force acting on a body of mass 7 kg produces an acceleration of 10 m/s².

We are asked to calculate the acceleration that the same force will produce in a body of mass 9 kg.

In order to calculate the acceleration that the same force will produce in a body of mass 9 kg, we need to calculate the force acting on a body of mass 7 kg which produces an acceleration of 10 m/s².

Case 1 :

• Mass of the object $\rm (m_1)$ = 7 kg
• Acceleration $\rm (a_1)$ = 10 m/s²
• Force $\rm (F_1)$ = ?

As we know that,

⇒ F = ma

• F denotes force
• m denotes mass
• a denotes acceleration

⇒ F₁ = m₁ × a₁

⇒ F₁ = 7 kg × 10 m/s²

⇒ F₁ = 70 kg.m/s²

⇒ F₁ = 70 N

∴ Force acting on a body of mass 7 kg which produces an acceleration of 10 m/s² is 70 N.

Case 2 :

Now, as per the question, in the second case the force is same. We have to find the acceleration that the same force will produce in a body of mass 9 kg.

• Mass of the object $\rm (m_2)$ = 7 kg
• Acceleration $\rm (a_2)$ = ?
• Force $\rm (F_2)$ = 70 N

As we know that,

⇒ F = ma

• F denotes force
• m denotes mass
• a denotes acceleration

⇒ F₂ = m₂ × a₂

⇒ 70 N = 9 kg × a₂

⇒ 70 kg.m/s² ÷ 9 kg = a₂

⇒ $\bf 7.\overline{7}$ m/s² = a₂

∴ The acceleration that the same force will produce in a body of mass 9 kg will be $\bf 7.\overline{7}$ m/s².

Answer 2

Answer:-

• Mass=7kg=m1
• Acceleration=a1=10m/s^2
• Mass=m2=9kg
• Acceleration=a2=?

Here Force is constant

• According to Newtons Second law

$\boxed{\sf Force=Mass\times Acceleration}$

$\\ \rm\longmapsto m_1\times a_1=m_2\times a_2$

$\\ \rm\longmapsto 7\times 10=9a_2$

$\\ \rm\longmapsto 70=9a_2$

$\\ \rm\longmapsto a_2=\dfrac{70}{9}$

$\\ \rm\longmapsto a_2=7.7m/s^2$