આકૃતિમાં દર્શાવ્યા પ્રમાણે 2 kg દળના બ્લોકને | vedclass

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Question

${W_c}\, + \,{W_{nc}}\, + \,\,{W_{ext}}\,\, = \,\,\,\Delta KE$

$ \Rightarrow \,\,\,mg(0.5\,\, + \,\,x)\sin {30^ \circ }\, - \,\,\mu mg\,(0.5\,\, +

Vedclass · Accepted Answer

$34.67 $

Vedclass · Answer

${W_c}\, + \,{W_{nc}}\, + \,\,{W_{ext}}\,\, = \,\,\,\Delta KE$

$ \Rightarrow \,\,\,mg(0.5\,\, + \,\,x)\sin {30^ \circ }\, - \,\,\mu mg\,(0.5\,\, + \,\,x)\,\cos {30^ \circ }\, - \,\,\frac{1}{2}k{x^2}\, = \,\,0$

$ \Rightarrow \,\,\,2\,\, 	imes \,\,10(0.5\,\, + \,\,x)\,\frac{1}{2}\,\, - \,\,0.3\,\, 	imes \,\,2\,\, 	imes \,\,10\,\,(0.5\,\, + \,\,x)\,\frac{{\sqrt 3 }}{2}\,\, - \,\,\frac{1}{2}\,\, 	imes \,\,4000{x^2}\, = \,\,0$

$ \Rightarrow \,\,20(0.5\,\, + \,\,x)\,\, - \,\,6(0.5\,\, + \,\,x)\,\sqrt 3 \,\, - \,\,4000\,{x^2}\, = \,\,0$

$ \Rightarrow \,\,\,10\,\, + \,\,20x\,\, - \,\,(3\,\, + \,\,6x)\,\sqrt 3 \,\, - \,\,4000\,\,{x^2}\, = \,\,0$

$ \Rightarrow \,\,\,10\,\, + \,\,20x\,\, - \,\,3\,\,\sqrt 3 \,\, - \,\,6\,\,\sqrt 3 \,x\,\, - \,\,4000{x^2}\, = \,\,0$

$ \Rightarrow \,\,\,4.8\,\, + \,\,9.6x\,\, - \,\,4000\,\,{x^2}\, = \,\,0\,\,\,\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,4000\,\,{x^2}\, - \,\,0.6\,\,x\,\, - \,\,4.8\,\, = \,\,0$

$x\,\, = \,\,\,\frac{{9.6\,\, \pm \,\,\,\sqrt {{{(9.6)}^2}\, + \,\,4(4.8)\,\,(4000)} }}{{2\,\, 	imes \,\,4000}}\,\, = \,\,0.03467\,\,m\,\, = \,\,34.67\,\,\,mm$

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