{"result":{"text":"table attributes columnalign left end attributes row cell d U equals left parenthesis d m right parenthesis g space space space space space space space space space space space space y equals open parentheses fraction numerator 2 m over denominator pi R end fraction R d theta close parentheses space g R left parenthesis 1 minus cos theta right parenthesis end cell row cell therefore U equals integral from 0 to pi divided by 2 of fraction numerator 2 m g R over denominator pi end fraction left parenthesis 1 minus cos theta right parenthesis d theta end cell row cell space space space space space space space space equals fraction numerator 2 m g R over denominator pi end fraction left square bracket theta minus sin theta right square bracket to the power of pi divided by 2 end exponent end cell row cell space space space space space space space space equals fraction numerator 2 m g R over denominator pi end fraction left square bracket left parenthesis pi divided by 2 minus sin pi divided by 2 right parenthesis minus left parenthesis 0 minus sin 0 right square bracket end cell row cell space space space space space space space space equals fraction numerator m g R over denominator pi end fraction left square bracket pi minus 2 right square bracket end cell row cell T h u s space 1 half m v squared equals fraction numerator m g R over denominator pi end fraction left parenthesis pi minus 2 right parenthesis end cell row cell therefore v equals square root of 2 g R open parentheses 1 minus 2 over pi close parentheses end root end cell end table"},"status":"ok"}