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A force of 5 N produces an acceleration of 8 ms-² on a mass
m_1 and an acceleration of 24 ms-² on a mass m². What acceleration would the same force provide if both the masses are tied together?

Hoping for gööd Answer! :D​

Answer 1

Explanation:

Correct answer is 6

From Newton's second law of motion, the applied force is directly proportional to the acceleration produced or F=ma

The unit of force is newton in SI denoted by the symbol N.

Forces acting on a mass m

1

with acceleration a

1

and mass m

2

with acceleration a

2

are as given below.

m

1

=

a

1

F

=

8

5

kg.

m

2

=

a

2

F

=

24

5

kg.

M=(

8

5

+

24

5

)kg=(

6

5

)kg

Acceleration produced in M (when the two masses are tied together),

a=

M

F

=

6

5

5

=6 ms

−2

Answer 2

❒ Given :-

• A force of 5 N produces an acceleration of 8 m/s-² on a mass m¹ .
• And an acceleration of 24 m/s-² on a mass m².

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❒ To Find :-

• What will be the acceleration if they are tied together .

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❒ Formula Used :-

Force :

${\large{\red{\bigstar \: \: \: \: {\blue{\underbrace{\underline{\orange{\bf{F = M \times A}}}}}}}}}$

Mass :

${\large{\red{\bigstar \: \: \: \: {\blue{\underbrace{\underline{\orange{\bf{ M = \frac{F}{A} }}}}}}}}}$

${{\pink{➵}}{\underline{\text{Here:}}}}$

• ➻ M = Mass = M¹ , M²
• ➻ F = Force = 5 N
• ➻ A = Acceleration = 8 m/s-² , 24 m/s-²

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❒ Solution :-

${{\pink{➵}}{\underline{\text{First finding the masses of both the objects :}}}}$

Mass of M¹ :

${\large{:{\longmapsto{\bf{M{\small_{1}} = \frac{F}{A{\small_{1}}} }}}}}$

${\large{\purple{:{\longmapsto{\underline{\boxed{\bf{{M{\small_{1}} = \frac{5}{8} \: kg}}}}}}</p><p>}}}$

Mass of M² :

${\large{:{\longmapsto{\bf{M{\small_{2}} = \frac{F}{A{\small_{2}}} }}}}}$

${\large{\purple{:{\longmapsto{\underline{\boxed{\bf{{M{\small_{2}} = \frac{5}{24} \: kg}}}}}}</p><p>}}}$

${{\pink{➵}}{\underline{\text{Acceleration if they are tied together :}}}}$

• ➻Force = 5 N
• ${\bf{➻{ \frac{5}{8} + \frac{5}{24} ={\cancel \frac{20}{24} = \frac{5}{6} } }}}$

${\large{\twoheadrightarrow{\bf{F = M \times A}}}}$

${\large{\twoheadrightarrow{\bf{ A = \frac{F}{M} }}}}$

${\large{\twoheadrightarrow{\bf{ A = \frac{\cancel{5}}{( \frac{\cancel{5}}{6}) } }}}}$

${\large{\orange{:{\longmapsto{\blue{\underline{\boxed{\bf{A = 6 m/s -²}}}}}}}}}$

${{\pink{➵}}{\underline{\text{Hence:}}}}$

${\large{\purple{\underline{\green{\underline{\red{\mathfrak{\pmb{Acceleration = 6m/s -²}}}}}}}}}$

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