Question-22872

Question Number 22872 by Physics lover last updated on 23/Oct/17

Commented by ajfour last updated on 23/Oct/17

Commented by ajfour last updated on 24/Oct/17

I_{d i s c} = \frac{{M R}^{2}}{2}

\Rightarrow M = \frac{2 I}{R^{2}} = \frac{2 \times 0.16}{(1 / 25)} k g = 8 k g

T h e a c c . o f r o p e o n l e f t o f d i s c

i s = a = \frac{a}{2} + α R

\Rightarrow \boldsymbol α R = \frac{\boldsymbol a}{2} \dots . (i)

\boldsymbol T_{2} - \boldsymbol m g = \boldsymbol m a \dots (i i)

(\boldsymbol T_{1} - \boldsymbol T_{2}) \boldsymbol R = \boldsymbol I α \dots (i i i)

\boldsymbol M g - \boldsymbol T_{1} - \boldsymbol T_{2} = \frac{\boldsymbol M a}{2} \dots (i v)

F r o m (i i i) :

\Rightarrow T_{1} = T_{2} + \frac{I α R}{R^{2}} = T_{2} + \frac{I a}{2 R^{2}}

f r o m (i v) :

M g - T_{2} - T_{2} - \frac{I a}{2 R^{2}} = \frac{M a}{2}

\Rightarrow M g - 2 m g - 2 m a - \frac{I a}{2 R^{2}} = \frac{M a}{2}

\Rightarrow \boldsymbol a = \frac{(\boldsymbol M - 2 \boldsymbol m) \boldsymbol g}{(\frac{\boldsymbol M}{2} + 2 \boldsymbol m + \frac{I}{2 \boldsymbol R^{2}})}

= \frac{(8 - 2) (10)}{(4 + 2 + 2)} m / s^{2} = \frac{15}{2} \boldsymbol m / \boldsymbol s^{2}

\Rightarrow \frac{30}{x} = \frac{15}{2} o r \boldsymbol x = 4 .

Commented by Physics lover last updated on 24/Oct/17

b u t t h e a n s w e r g i v e n i s 4 .

? ? ?

Commented by Physics lover last updated on 24/Oct/17

i h a v g o t i t . A n y w a y s, t h a n k y o u s i r .

W i t h o u t u r h i n t s i c u d n t h a v s o l v e d

i t .

Answered by Physics lover last updated on 24/Oct/17

T r a n s l a t i o n :

T_{2} = 1 (a + g) \dots i

&

8 g - T_{1} - T_{2} = 8 (\frac{a}{2})

\Rightarrow T_{1} = 7 g - 5 a \dots i i

R o t a t i o n :

T_{1} R - T_{2} R = I α

\Rightarrow T_{1} R^{2} - T_{2} R^{2} = I α R = I (\frac{a}{2})

\Rightarrow T_{1} - T_{2} = 2 a \dots i i i

s u b s t i t u t i n g T_{2} f r o m e q \dots i

a n d T_{1} f r o m e q \dots i i i n e q \dots i i i

\Rightarrow 7 g - 5 a - a - g = 2 a

\Rightarrow \frac{6 g}{8} = a = \frac{6 (10)}{8} = \frac{30}{4}

\Rightarrow x = 4