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mechanics

Easy

Question

$I f space m space left parenthesis g plus pi n r squared right parenthesis space a n d space m left parenthesis g plus pi n r right parenthesis space r e p r e s e n t space r a d i a l space a n d space tan g e n t i a l space a c c e l e r a t i o n s comma space t h e space m o t i o n space o f space a space p a r t i c l e space w i l l space b e space u n i f o r m l y space c i r c u l a r space i f$

$10 (\sqrt{5} - 1) J a n d 2 m g ⥂ r = 2 \times 1 \times 10 \times 1 = 20 J$
$= m \{g + (4 π^{2} {(\frac{n}{60})}^{2} r)\} = m \{g + (\frac{π^{2} n^{2} r}{900})\} but h = \frac{5}{2} r$
$m \{g + (π^{2} n^{2} r) / 900\} and T = m g + m ω^{2} r = m \{g + 4 π^{2} n^{2} r\}$
$r = \frac{2}{5} \times h = \frac{2}{5} \times 5 = 2 metre but 4 \sqrt{5} J$

The correct answer is: $r = \frac{2}{5} \times h = \frac{2}{5} \times 5 = 2 metre but 4 \sqrt{5} J$

$I n space u n i f o r m space c i r c u l a r space m o t i o n space tan g e n t i a l space a c c e l e r a t i o n space r e m a i n s space z e r o space b u t space m a g n i t u d e space o f space r a d i a l space a c c e l e r a t i o n space r e m a i n s space c o n s tan t.$

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