Figure shows a body of mass m moving with a uniform speed $v$ along a circle of radius $r$. The change in velocity in going from $A$ to $B$ is

19-43

  • A

    $v\sqrt 2 $

  • B

    $v/\sqrt 2 $

  • C

    $v$

  • D

    zero

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Establish the following vector inequalities geometrically or otherwise:

$(a)$ $\quad| a + b | \leq| a |+| b |$

$(b)$ $\quad| a + b | \geq| a |-| b |$

$(c)$ $\quad| a - b | \leq| a |+| b |$

$(d)$ $\quad| a - b | \geq| a |-| b |$

When does the equality sign above apply?

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  • [AIPMT 1988]

The resultant of $\overrightarrow A + \overrightarrow B $ is ${\overrightarrow R _1}.$ On reversing the vector $\overrightarrow {B,} $ the resultant becomes ${\overrightarrow R _2}.$ What is the value of $R_1^2 + R_2^2$