Question

A force of 5N gives a mass $m _ { 1 }$ and acceleration of $\bold {8m/s^2}$, and a mass $m _ { 2 }$ an acceleration of $\bold {24m/s^2}$. What acceleration would it give if both the masses are tied together?​

Answer 1

Answer :-

The force would give an acceleration of 6 m/s² if both the masses are tied together .

Explanation :-

For mass (m₁) :-

→ Force (F) = 5 N

→ Acceleration (a₁) = 8 m/s²

So, mass (m₁) according to 2nd law of motion will be :-

⇒ F = m₁a₁

⇒ 5 = m₁ × 8

⇒ m₁ = 5/8

For mass (m₂) :-

→ Force (F) = 5 N

→ Acceleration (a₂) = 24 m/s²

⇒ F = m₂a₂

⇒ 5 = m₂ × 24

⇒ m₂ = 5/24

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When the two masses are tied together, the resultant mass will be (m₁ + m₂) . As given force is 5 N only, so now let's calculate the acceleration (a) by the 2nd law of motion .

⇒ F = a(m₁ + m₂)

⇒ 5 = a(5/8 + 5/24)

⇒ 5 = a(5/6)

⇒ a = 5/(5/6)

⇒ a = 6 m/s²

Answer 2

Answer:

Given :-

• A force of 5N gives a mass of m₁ an acceleration of 8 m/s² and a mass of m₂ an acceleration of 24 m/s².

To Find :-

• What acceleration would it give if both the masses are tied together.

Formula Used :-

$\clubsuit$ Force Formula :

$\mapsto \sf\boxed{\bold{\pink{F =\: ma}}}$

where,

• F = Force
• m = Mass
• a = Acceleration

Solution :-

${\small{\bold{\purple{\underline{\bigstar\: In\: the\: first\: case\: of\: mass\: :-}}}}}$

Given :

❒ Force (F) = 5N

❒ Acceleration (a₁) = 8 m/s²

According to the question by using the formula we get,

$\implies \sf F =\: m_1a_1$

$\implies \sf 5 =\: m_1 \times 8$

$\implies \sf \dfrac{5}{8} =\: m_1$

$\implies \sf 0.625 =\: m_1$

$\implies \sf\bold{\green{m_1 =\: 0.625\: kg}}$

Again,

${\small{\bold{\purple{\underline{\bigstar\: In\: second\: case\: of\: mass\: :-}}}}}$

Given :

❒ Force (F) = 5N

❒ Acceleration (a₂) = 24 m/s²

According to the question by using the formula we get,

$\implies \sf F =\: m_2a_2$

$\implies \sf 5 =\: m_2 \times 24$

$\implies \sf \dfrac{5}{24} =\: m_2$

$\implies \sf 0.208 =\: m_2$

$\implies \sf\bold{\green{m_2 =\: 0.208\: kg}}$

Now, we have to find the total mass :

Given :

❒ Mass (m₁) = 0.625 kg

❒ Mass (m₂) = 0.208 kg

Then,

$\implies \sf Total\: mass =\: m_1 + m_2$

$\implies \sf Total\: mass =\: 0.625 + 0.208$

$\implies \sf \bold{\green{Total\: mass =\: 0.833\: kg}}$

Now, we have to find the acceleration would it give if both the masses are tied together :

Given :

❒ Force (F) = 5N

❒ Mass (m) = 0.833 kg

According to the question by using the formula we get,

$\longrightarrow \sf F =\: ma$

$\longrightarrow \sf \dfrac{F}{m} =\: a$

$\longrightarrow \sf \dfrac{5}{0.833} =\: a$

$\longrightarrow \sf 6 =\: a$

$\longrightarrow \sf\bold{\red{a =\: 6\: m/s^2}}$

$\therefore$ The acceleration would it give if both the masses are tied together is 6 m/s².