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# S1: If the accelerating potential of an electron is doubled then its velocity becomes 1.4 times. S2: It will move on a circular path with same velocity.

$\begin{array}{1 1} \text{(a) S1 is true, S2 is true; S2 is correct explanation of S1.} \\ \text{(b) S1 is true, S2 is true; S2 is not correct explanation of S1.} \\ \text{(c) S1 is false; S2 is true.} \\ \text{(d) S1 is true; S2 is false.} \end{array}$

Ans : (d)
If V is the accelerating potential and v is the velocity of electron, then
$eV = \large\frac{1}{2} mv^2$
$v \sim \sqrt V$
$\Rightarrow \large\frac{v_1}{v_2} = \sqrt { \bigg( \large\frac{V_1}{V_2} \bigg) }$
Here, $V_1 = V, V_2 = 2V; v_1 = v$
So, $\large\frac{v}{v_2} = \sqrt { \large\frac{V}{2V} }= \large\frac{1}{ \sqrt 2}$
$\Rightarrow v_2 = \sqrt 2v = 1.4v$

edited Mar 13, 2014