Question

A force of 72 dyne is inclined to the horizontal at an angle of 60°. Find the acceleration in a mass of 9 g,
which moves in a horizontal direction.

Answer 1

Answer:-

Acceleration in the mass is 0.04 m/s² [In S.I. unit]  

Explanation:-  

Here, we are given that a force of 72 dyne is inclined to horizontal at an angle of 60°.

So, firstly let's convert the units of force and mass of the body to S.I. unit.

 Force :-

⇒ 1 dyne = 10⁻⁵ N

⇒72 dyne = 72 × 10⁻⁵

⇒ 7.2×10⁻⁴ N  

Mass :-  

⇒ 1 g = 10⁻³ kg

⇒ 9g = 9×10⁻³ kg

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Since the force is inclined at an angle to the horizontal, thus horizontal component of the force will be :-  

Fₓ = F × cosθ

⇒ Fₓ = 7.2×10⁻⁴×cos60°

⇒ Fₓ = 7.2×10⁻⁴×0.5

⇒ Fₓ = 3.6×10⁻⁴ N

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Now, according to Newton's 2nd law of motion, acceleration of the mass will be :-  a = Fₓ/m

⇒ a = [3.6×10⁻⁴]/[9×10⁻³]

⇒ a = 0.4/10

⇒ a = 0.04 m/s²

Answer 2

$\Large{\underbrace{\underline{\bf{TO\: FIND\::}}}}$

• The acceleration of the mass.

$\Large{\underbrace{\underline{\bf{GIVEN\::}}}}$

• 72 dyne force (F) is inclined to the horizontal at 60°.

• Mass = 9 g

$\Large{\underbrace{\underline{\bf{SOLUTION\::}}}}$

☛ Refer the attachment free body diagram.

✰ Component of force along horizontal $({\bf{F_x}})$ given as,

➵ $\sf{F_x\:=\:F\:\cos{60}}$

➵ $\sf{F_x\:=\:72\times{\dfrac{1}{2}}}$

➵ $\bf{F_x\:=\:36\:dyne}$

As we know that,

$\orange\bigstar\:\mid{\bf{\blue{Force\:=\:Mass\times{Acceleration}}}}\:\mid\:\green\bigstar$

➳ $\sf{36\:=\:9\times{Acceleration}}$

➳ $\sf{Acceleration\:=\:\dfrac{36}{9}}$

➳ $\sf\pink{Acceleration\:=\:4\:cm/s^{2}}$

∴ The acceleration of the mass is 4 cm/s².