Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

A cyclotron is used to accelerate protons. If the operating magnetic field is $1.0 \mathrm{~T}$ and the radius of the cyclotron 'dees' is $60 \mathrm{~cm}$ , the kinetic energy of the accelerated protons in $\mathrm{MeV}$ will be :
[ use $\mathrm{m}_{\mathrm{p}}=1.6 \times 10^{-27} \mathrm{~kg}, \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}$ ]
Option: 1
$12$

Option: 2
$18$

Option: 3
$16$

Option: 4
$32$

Answers (1)

best_answer

$\mathrm{B=1T}$

$\mathrm{r=60 cm}$

$\mathrm{r=\frac{mv}{qB}}$

$\mathrm{P=mv=qBr}$

Kinetic energy of the accelerated protons is

$\mathrm{K E =\frac{p^2}{2 m}=\frac{q^2 B^2 r^2}{2 m} }$

$\mathrm{=\frac{(\left.1.6 \times 10^{-19}\right)^2 \times(1)^2 \times(0.36)}{2 \times 1.6 \times 10^{-27}} }$

$\mathrm{=\frac{1.6 \times 0.36 \times 10^{-38}}{2 \times 10^{-27}} }$

$\mathrm{K E =\frac{1.6 \times 0.18 \times 10^{-11} }{1.6 \times 10^{-13}}MeV }$

$\mathrm{K E =18 \mathrm{MeV}}$

Hence 2 is correct option

\end{aligned}

Posted by

Info Expert 30

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

5 g of Na₂SO₄ was dissolved in x g of H₂O. The change in freezing point was found to be 3.82⁰C. If Na₂SO₄ is 81.5% ionised, the value of x (K

A capacitor is made of two square plates each of side 'a' making a very small angle $\alpha$

A solution of m-chloroaniline, m-chlorophenol and m-chlorobenzoic acid in ethyl acetate was extracted initially with a saturated solution of NaHCO₃ to give fraction A. The leftover organic phase was extracted with d

Trending Articles/News

anam-khan

AESL expands Aakash Digital 2.0 to offer AI-powered coaching for NEET, JEE, Olympiads

anam-khan

Bihar Board extends BSEB Super 50 free coaching application last date to March 26

anam-khan

JEE Main City Intimation Slip 2025 Live: NTA session 2 exam city slips soon at jeemain.nta.nic.in

Latest Question