If energy (E), velocity (v) and time (T) are chosen  as the fundamental quantities, the dimensional formula of surface tension will be

• [Ev^-2T^-1]

• [Ev^-1T^-2]

• [Ev^-2T^-2]

• [E^-2v^-1T^-3]

C.

[Ev^-2T^-2]

A particle of unit mass undergoes one-dimensional motion such that its velocity according to
V(x) =  βx^-2n where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x is given by 

• -2nβ² x^-2n-1

• -2nβ² x^-4n-1

• -2β x^-2n+1
  

• -2nβ²e^-4n+1

Two similar springs P and Q have spring constants K_P and KQ, such that K_P>K_Q. They are stretched, first by the same amount (case a), then by the same force (case b). The work done by the springs W_P and W_Q are related as, in  case (a) and case (b), respectively

• W_P =W_Q ;W_P> W_Q

• W_P =W_Q ;W_P= W_Q

• W_P > W_Q ;W_Q> W_P

• W_P <W_Q ; W_P< W_Q

A block of mass 10 kg, moving in the x-direction with a constant speed of 10 ms^-1 , is subjected to a retarding force F= 0.1x J/m during its travel from x = 20 m to 30 m. Its final KE will be

• 475 J

• 450 J

• 275 J

• 250 J 

A particle of mass m is driven by a machine that delivers a constant power K watts. If the particle starts from rest, the force on the particle at time t is

• 
• 
• 
• 

A.

As the machine delivers a constant power
So F, v =constant = k (watts)