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Question

$\overrightarrow{ r }=10 \alpha t ^{2} \hat{ i }+5 \beta( t -5) \hat{ j }$

$\overrightarrow{ v }=20 \alpha t \hat{ i }+5 \beta \hat{ j }$

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Vedclass · Accepted Answer

$10$

Vedclass · Answer

$\overrightarrow{ r }=10 \alpha t ^{2} \hat{ i }+5 \beta( t -5) \hat{ j }$

$\overrightarrow{ v }=20 \alpha t \hat{ i }+5 \beta \hat{ j }$

$\overrightarrow{ L }= m (\overrightarrow{ r } 	imes \overrightarrow{ v })$

$=m\left[10 \alpha t ^{2} \hat{ i }+5 \beta( t -5) \hat{ j }ight] 	imes[20 \alpha t \hat{ i }+5 \beta \hat{ j }]$

$\overrightarrow{ L }= m \left[50 \alpha \beta t ^{2} \hat{ k }-100 \alpha \beta\left( t ^{2}-5 t ight) \hat{ k }ight]$

At $t =0, \overrightarrow{ L }=\overrightarrow{0}$

$50 \alpha \beta t ^{2}-100 \alpha \beta\left( t ^{2}-5 t ight)=0$

$t -2( t -5)=0$

$t=10 \sec$

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