Question

a force acting on a body of mass 10 kg produce an acceleration of 17.5m/s² what acceleration the same force Will produce in a body of mass 8 kg​

Answer 1

Answer:

21.875 m/s²

Explanation:

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

• A force acting on a body of mass 10 kg produce an acceleration of 17.5 m/s².

We are asked to calculate what acceleration the same force will produce in a body of mass 8 kg.

In order to calculate the what acceleration the same force will produce in a body of mass 8 kg, we need to calculate the force acting on a body of mass 10 kg which produce an acceleration of 17.5 m/s².

In first case,

• Mass of the object (m)= 10 kg
• Acceleration (a) = 17.5 m/s²
• Force (F) = ?

As we know that,

$\longmapsto \bf{F = ma }$

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

$\longmapsto \rm {F = 10 \; kg \times 17.5 \; ms^{-2} }$

$\longmapsto \rm {F = 10 \; kg \times \dfrac{175}{10} \; ms^{-2} }$

$\longmapsto \rm {F = 175 \; kg. ms^{-2} }$

$\longmapsto \bf {F = 175 \; N }$

∴ 175 N of force is acting on a body of mass 10 kg which produce an acceleration of 17.5m/s².

In second case,

We have to find that what acceleration the same force will produce in a body of mass 8 kg. Thus, force will remain same in this case. We have,

• Force (F) = 175 N
• Mass (m) = 8 kg
• Acceleration (a) = ?

As we know that,

$\longmapsto \bf{F = ma }$

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

$\longmapsto \rm {175 \; N = 8 \; kg \times a}$

$\longmapsto \rm {175 \; kg. ms^{-2} = 8 \; kg \times a}$

$\longmapsto \rm {\cancel{ \dfrac{175 \; kg. ms^{-2}}{8 \; kg}} = a}$

$\longmapsto \bf { 21.875 \; ms^{-2}= a}$

∴ The same force will produce the acceleration of 21.875 m/s² in a body of mass 8 kg.

Answer 2

Answer:-

• Mass=m1=10kg
• Mass=m2=8kg
• Acceleration=a1=17.5m/s^2
• Acceleration=a2=?.

Here Force is constant

• According to Newtons second law

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

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

$\\ \sf \longmapsto 10\times 17.5=8a_2$

$\\ \sf \longmapsto 175=8a_2$

$\\ \sf \longmapsto a_2=\dfrac{175}{8}$

$\\ \sf \longmapsto a_2=21.8m/s^2$