Question

A particle of mass 'm' is subjected to a force

= F₀ (cos t + sin t $\hat { \mathrm { j } }$ ). If initially (t = 0) the particle is at rest, then K.E. of particle as a function of time is given by –

• A. $\frac { \mathrm { F } _ { 0 } ^ { 2 } } { \mathrm {~m} }$(1 – cos 2t)
• B. $\frac { \mathrm { F } _ { 0 } ^ { 2 } } { \mathrm {~m} }$(1 – cos t)
• C. $\frac { \mathrm { F } _ { 0 } ^ { 2 } } { \mathrm {~m} }$sin t
• D. $\frac { \mathrm { F } _ { 0 } ^ { 2 } } { \mathrm {~m} }$.t

Answer 1

Answer: (B)

$\frac { \mathrm { F } _ { 0 } ^ { 2 } } { \mathrm {~m} }$(1 – cos t)

Answer 2

$\vec { a } = \frac { \vec { F } } { m } = \frac { F _ { 0 } } { m }$ (cos t + sin t)

\ = {sin t + (1– cos t)}

\ K.E. = $\frac { 1 } { 2 }$m = $\frac { \mathrm { F } _ { 0 } ^ { 2 } } { \mathrm {~m} }$ (1– cos t)