Question

A particle of mass m is moving in a circular path of constant radius r such that, its centripetal acceleration ac is varying with time t as ac = k²rt², where k is a constant. The power delivered to the particle by the forces acting on it is ______.

Options

• mk²rt²

• mk²r²t

• mkrt

• mkr²t²

Answer 1

A particle of mass m is moving in a circular path of constant radius r such that, its centripetal acceleration ac is varying with time t as ac = k²rt², where k is a constant. The power delivered to the particle by the forces acting on it is mk²r²t.

Explanation:

centripetal acceleration ac = k²rt²

or, `"v"^2/"r" = "k"^2"rt"^2`    (given)

∴ v = krt 

∴ `"a"_"t" = "dv"/"dt" = "d"/"dt" "krt" = "kr"` 

∴ Power P = F_tV = ma_tV = mkr · krt = mk²r²t