A body of mass 1 kg begins to move unde...

A body of mass `1 kg` begins to move under the action of a time dependent force `vec F = (2 t hat I + 3 t^(2) hat j) N`, where `hat i` and `hat j` are unit vectors along x-and y-axes. What power will be developed by the force at the time `t` ?

`(2t^(2)+4t^(4))W`

`(2t^(3)+3t^(4))W`

`(2t^(3)+3t^(5))W`

`(2t+3t^(3))W`

Text Solution

Verified by Experts

The correct Answer is:

(C ) According to question, a body of mass 1 kg begins to move under the action of time dependent force,
`F=(2thati+3t^(2)hatj)N`
`m(dv)/(dt)=2thati+3t^(2)hatj`
`int dv=int(2thati+3t^(2)hatj)dt`
`v=t^(2)hati+t^(3)hatj`
`:.` Power developed by the force at the time t will be given as
`P=F.v=(2thati+3t^(3)hatj).(t^(2)hati+t^(3)hatj)=(2t.t^(2)+3t^(2).t^(3))` lt `P=(2t^(3)+3t^(5))W`

Topper's Solved these Questions

WORK, ENERGY AND POWER
DC PANDEY|Exercise MATCH THE COLUMNS|7 Videos
WORK, ENERGY & POWER
DC PANDEY|Exercise Level 2 Comprehension Based|2 Videos
WORK, POWER AND ENERGY
DC PANDEY|Exercise E Integer Type Questions|11 Videos

A body of mass 1 kg begins to move under the action of a time dependent force F=(2that(i)+3t^(2)hat(j))N, "where" hat(i)and hat(j) are unit vector along x and y axis. What power will be developed by the force at the time?

`(2t^(3)+3t^(4)) W`

`(2t^(3)+3t^(5)) W`

`(2t^(2)+3t^(2)) W`

`(2t^(2)+3t^(4)) W`

A body of mass 1kg begins to move under the actio of a time dependent force vec(F)=(2t hat(i)+3t^(2) hat(j))N , where hat (i) and hat(j) are unit vectors along X and Y axis. What does will be developed by the source at time t ?

`(2t^(2)+4r^(4))W`

`(2t^(2)+3r^(4))W`

`(2t^(3)+3r^(5))W`

`(2t+3r^(3))W`

The angle which the vector vec(A)=2hat(i)+3hat(j) makes with the y-axis, where hat(i) and hat(j) are unit vectors along x- and y-axis, respectively, is

`cos^(-1)(3//5)`

`cos^(-1)(2//3)`

`tan^(-1)(2//3)

`sin^(-1)(2//3)`