An α -particle of mass 6.4 × 10-27 kg and charge 3.2 × 10-19 C is situated in a uniform electric field of 1.6 × 105 Vm -1 . The velocity of the particle at the end of 2 × 10-2 m path when it starts from rest is

Question

An α -particle of mass 6.4 × 10-27 kg and charge 3.2 × 10-19 C is situated in a uniform electric field of 1.6 × 105 Vm -1 . The velocity of the particle at the end of 2 × 10-2 m path when it starts from rest is (A) 2 √3 × 105 ms -1 (B) 8 × 105 ms -1 (C) 16 × 105 ms -1 (D) 4 √2 × 105 ms -1

Tardigrade Admin · Accepted Answer

Force on a charge particle placed in a uniform electric field is given as,

F = qE = m g

\Rightarrow E = \frac{m g}{q}

From equation of motion,

v^{2} = u^{2} + 2 a s = (0)^{2} + 2 a s

\Rightarrow v = \frac{2 qE}{m}

s = \frac{2 \times 3.2 \times 1 0 ^{- 19} \times 1.6 \times 1 0 ^{5}}{6.4 \times 1 0 ^{- 27}} \times 2 \times 1 0^{- 2}

\Rightarrow v = 42 \times 1 0^{5} m / s

Q. An $α$ -particle of mass $6.4 \times 1 0^{- 27} k g$ and charge $3.2 \times 1 0^{- 19} C$ is situated in a uniform electric field of $1.6 \times 1 0^{5} V m^{- 1} .$ The velocity of the particle at the end of $2 \times 1 0^{- 2} m$ path when it starts from rest is

$23 \times 1 0^{5} m s^{- 1}$

$8 \times 1 0^{5} m s^{- 1}$

$16 \times 1 0^{5} m s^{- 1}$

$42 \times 1 0^{5} m s^{- 1}$

Q. An α -particle of mass 6.4×10−27kg and charge 3.2×10−19C is situated in a uniform electric field of 1.6×105Vm−1. The velocity of the particle at the end of 2×10−2m path when it starts from rest is

23​×105ms−1

8×105ms−1

16×105ms−1

42​×105ms−1

Force on a charge particle placed in a uniform electric field is given as, F=qE=mg ⇒E=qmg​ From equation of motion, v2=u2+2as=(0)2+2as ⇒v=m2qE​​ s=6.4×10−272×3.2×10−19×1.6×105​×2×10−2​ ⇒v=42​×105m/s

Q. An $α$ -particle of mass $6.4 \times 1 0^{- 27} k g$ and charge $3.2 \times 1 0^{- 19} C$ is situated in a uniform electric field of $1.6 \times 1 0^{5} V m^{- 1} .$ The velocity of the particle at the end of $2 \times 1 0^{- 2} m$ path when it starts from rest is

$23 \times 1 0^{5} m s^{- 1}$

$8 \times 1 0^{5} m s^{- 1}$

$16 \times 1 0^{5} m s^{- 1}$

$42 \times 1 0^{5} m s^{- 1}$