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13.Oscillations
hard
$600 \,N/m $ બળ અચળાંક ધરાવતી સ્પ્રિંગ ધરાવતી બંદૂકમાં $15\, g$ નો બોલ મૂકીને $5\,cm$ દબાવીને મુકત કરતાં દડાની મહત્તમ અવધી કેટલી ..... $m$ થાય? ($g = 10\, m/s^2$)
A
$6.0$
B
$10.0$
C
$12.0$
D
$8.0$
Solution
(b) For getting horizontal range, there must be some inclination of spring with ground to project ball.
${R_{max}} = \frac{{{u^2}}}{g}$ …..(i)
But $K.E.$ acquired by ball $= P.E.$ of spring gun
$ \Rightarrow \frac{1}{2}m{u^2} = \frac{1}{2}k{x^2}$
==> ${u^2} = \frac{{k{x^2}}}{m}$…..(ii)
From equation (i) and (ii)
${R_{max}} = \frac{{k{x^2}}}{{mg}} = \frac{{600 \times {{(5 \times {{10}^{ – 2}})}^2}}}{{15 \times {{10}^{ – 3}} \times 10}}=10\,m.$
Standard 11
Physics
