A particle of mass m is projected at an angle α to the horizontal with an initial velocity u . The work done by gravity during the time it reaches its highest point is -

Question

A particle of mass m is projected at an angle α to the horizontal with an initial velocity u . The work done by gravity during the time it reaches its highest point is - (A)  textmu2 textsin2 α  (B) (m u2 c o s2 α /2) (C) (m u2 s i n2 α /2) (D) -(m u2 s i n2 α /2)

Tardigrade Admin · Accepted Answer

textW textg = - Δ textU Work done by gravity = decrease in potential energy mathrmW=- mathrmmgH=- mathrmmg(( mathrmu2 sin 2 α/2 mathrm~g)) = -(m u2 s i n2 α /2)

Q. A particle of mass $m$ is projected at an angle $α$ to the horizontal with an initial velocity $u$ . The work done by gravity during the time it reaches its highest point is -

$mu^{2} sin^{2} α$

$\frac{m u ^{2} co s ^{2} α}{2}$

$\frac{m u ^{2} s i n ^{2} α}{2}$

$- \frac{m u ^{2} s i n ^{2} α}{2}$

$W_{g} = - Δ U$
Work done by gravity = decrease in potential energy
$W = - mgH = - mg (\frac{u ^{2} s i n ^{2} α}{2 g})$
$= - \frac{m u ^{2} s i n ^{2} α}{2}$

Q. A particle of mass m is projected at an angle α to the horizontal with an initial velocity u . The work done by gravity during the time it reaches its highest point is -

mu2sin2α

2mu2cos2α​

2mu2sin2α​

−2mu2sin2α​