First slide

Rectilinear Motion

Question

An alpha particle enters a hollow tube of 4 m length with an initial speed of 1 km/s. It is accelerated in the tube and comes out of it with a speed of 9 km/s. The time for which it remains inside the tube is

Moderate

A

$8 \times 10^{- 3} s$
B

$80 \times 10^{- 3} s$
C

$800 \times 10^{- 3} s$
D

$8 \times 10^{- 4} s$

Solution

$\begin{array}{l} i n i t i a l v e l o c i t y = u = 1000 m / s; f i n a l v e l o c i t y = v = 9000 m / s; l e n g t h o f t u b e = 4 m \\ v^{2} = u^{2} + 2 a s \\ \Rightarrow (9000)^{2} - (1000)^{2} = 2 \times a \times 4 \\ \Rightarrow a = 10^{7} m / s^{2} \\ Now t = \frac{v - u}{a} \\ \Rightarrow t = \frac{9000 - 1000}{10^{7}} = 8 \times 10^{- 4} \sec \end{array}$

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