Question

An object of mass m is tied to a string of length l and a variable force F is applied to it which brings the string gradually at an angle x° with the vertical. Find the work done by force F.

Refer the Attachment

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Answer 1

Answer:

hope it helps you see the attachment for further information

Answer 2

${ \huge \bf { \mid{ \overline{ \underline{Correct \: Question}}} \mid}}$

An object of mass m is tied to a string of length l and a variable force F is applied to it which brings the string gradually at an angle θ with the vertical. Find the work done by force F.

$\huge{\bold{\underline{\underline{Answer}}}}$

$\huge{\bold{\underline{Given:-}}}$

• Angle through its rotated = θ.
• Force applied is F.
• Mass of the object = m
• Tension Is "T".

$\huge{\bold{\underline{Explanation:-}}}$

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#refer the attachment for figure.

In Δ ABC,

• AC = l
• AD = l

Applying Trigonometric ratios,

$\large{\boxed{\tt Cos \theta = \dfrac{AB}{AC}}}$

Substituting the values,

$\large{\tt \hookrightarrow cos \theta = \dfrac{AB}{l}}$

$\large{\tt \hookrightarrow AB = cos \theta \times l}$

$\large{\tt \hookrightarrow AB = l cos \theta}$

Now, We can see,

☆ BD = AD - AB

Substituting the values,

$\large{\tt \hookrightarrow BD = AD - AB}$

$\large{\tt \hookrightarrow BD = l - l cos \theta}$

$\large{\tt \hookrightarrow BD = l(1 - cos \theta)}$

But BD is height to which the body is raised.

$\large{\hookrightarrow{\underline{\underline{\tt h = l(1 - cos \theta)}}}}$

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From, Work done formula,

$\large{\boxed{\tt W = mgh}}$

Substituting the values,

$\large{\tt \hookrightarrow W = mg \times h}$

$\large{\tt \hookrightarrow W = mg \times l(1 - cos \theta)}$

$\huge{\boxed{\boxed{\tt W = mgl(1 - cos \theta) \: J}}}$

So, the Work done to move the body is mgl(1 - cosθ) Joules.

Hence derived!

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