Question

XTRA
EDIGE
Date :
Page :
parts of life
development
personality
spirut af
sportmanship disasline
from spirit obi dience
punctuality
for play
utilize our free time
relax
our mind
6
ا​

Answer 1

Answer :

Length = l

Mass = M

Radius = R

Speed = v

Time Period = ?

━━━━━━━━━━━━━━━━━━

\begin{gathered}\sf :\implies a = \sqrt{g^2+ {a_c}^2}\\\end{gathered}

:⟹a=

g

2

+a

c

2

\begin{gathered}\qquad\quad\dag\small\sf {a_c}^2 = \dfrac{v^2}{R}\\\end{gathered}

†a

c

2

=

R

v

2

\begin{gathered}\sf :\implies a = \sqrt{g^2+ {\bigg\lgroup\dfrac{v^2}{R}\bigg\rgroup}^2}\\\\\end{gathered}

:⟹a=

g

2

+

⎩

⎪

⎪

⎪

⎧

R

v

2

⎭

⎪

⎪

⎪

⎫

2

\begin{gathered}\sf :\implies a = \sqrt{g^2+ {\bigg\lgroup\dfrac{v^4}{R^2}\bigg\rgroup}^2}\\\end{gathered}

:⟹a=

g

2

+

⎩

⎪

⎪

⎪

⎧

R

2

v

4

⎭

⎪

⎪

⎪

⎫

2

When T is the time period of thr oscillation then we know that,

\begin{gathered}\sf :\implies T = 2\pi \sqrt{\dfrac{l}{a}}\\\\\end{gathered}

:⟹T=2π

a

l

\begin{gathered}\sf :\implies T = 2\pi \sqrt{\dfrac{l}{\sqrt{g^2+\dfrac{v^4}{R^2}}}}\\\\\end{gathered}

:⟹T=2π

g

2

+

R

2

v

4

l

\sf :\implies\pink{ T = 2\pi \sqrt{\dfrac{l}{g^2+\bigg\lgroup\dfrac{v^4}{R^2}\bigg\rgroup^{\frac{1}{2}}}}}:⟹T=2π

g

2

+

⎩

⎪

⎪

⎪

⎧

R

2

v

4

⎭

⎪

⎪

⎪

⎫

2

1

l