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Physics

General

Easy

Question

The masses and radius of earth and moon are M₁ ,R₁and M₂ R₂respectively. Their centres are d distance of apart. The minimum velocity with which a particle of mass should be projected from a point mid way between their centres so that it escapes to infinity is……

$2 \sqrt{\frac{G}{d} (M_{1} + M_{2})}$
$2 \sqrt{\frac{2 G}{d} (M_{1} + M_{2})}$
$2 \sqrt{\frac{G m}{d}} (M_{1} + M_{2})$
$2 \sqrt{\frac{G m (M_{1} + M_{2})}{d (R_{1} + R_{2})}}$

The correct answer is: $2 square root of G over d open parentheses M subscript 1 plus M subscript 2 close parentheses end root$

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physics-General

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$text If end text a with not stretchy bar on top equals ı with not stretchy bar on top plus 2 ȷ with not stretchy bar on top plus 3 k with not stretchy bar on top comma b with not stretchy bar on top equals negative ı with not stretchy bar on top plus 2 ȷ with not stretchy bar on top plus k with not stretchy bar on top comma c with not stretchy bar on top equals 3 ı with not stretchy bar on top plus ȷ with not stretchy bar on top text and end text a with not stretchy bar on top plus t b with not stretchy bar on top$ is perpendicular to $stack c with ‾ on top$ , then $t equals$

For this question, we should know the rules of dot product.

$text If end text a with not stretchy bar on top equals ı with not stretchy bar on top plus 2 ȷ with not stretchy bar on top plus 3 k with not stretchy bar on top comma b with not stretchy bar on top equals negative ı with not stretchy bar on top plus 2 ȷ with not stretchy bar on top plus k with not stretchy bar on top comma c with not stretchy bar on top equals 3 ı with not stretchy bar on top plus ȷ with not stretchy bar on top text and end text a with not stretchy bar on top plus t b with not stretchy bar on top$ is perpendicular to $stack c with ‾ on top$ , then $t equals$

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