A particle is projected making an angle of 45° with horizontal having kinetic energy K. The kinetic energy at highest point will be ____________.

(a)

\(\frac{K}{\sqrt 2}\)

(b)

\(\frac{K}{2}\)

(c)

2K

(d)

k

If \(\vec F=(60\hat i+15\hat j-3\hat k)\)N and \(\vec v=(2\hat i-4\hat j+5\hat k)\) m/s, then instantaneous power is ___________.

(a)

195 watt

(b)

45 watt

(c)

75 watt

(d)

100 Watt

A mass of 1 kg is thrown up with a velocity of 1.00 m/s. After 5 seconds, it explodes into two parts. One part of mass 400 g comes down with a velocity 25 m/s. The velocity of other part is (Take g = 10 ms^-2)

(a)

40 m/s

(b)

40 m/s

(c)

100 m/s

(d)

60 m/s

Two bodies with kinetic energies in the ratio of 4: 1 are moving with equal linear momentum. The ratio of their masses is _______________.

(a)

4: 1

(b)

1:1

(c)

1:2

(d)

1:4

A force acts on a 3 g particle, in such a way that the position of the particle as a function of time is given by x = 3t - 4t² + t³, where x is in metres and t is in seconds. The work done during the first 4 second is _____________.

(a)

490 mJ

(b)

450 mJ

(c)

576 mJ

(d)

530 mJ