(A) workdone by all forces( both real and pseudo ) in 1 sec in frame of A is 0.5 J - True
acceleration a = Force/mass = 1N/1kg = 1m/s2
distance travelled (started from rest ) in 1 s= (1/2)at2 = (1/2)(1)(12) = 0.5m
workdon = force × distance = 1×0.5 = 0.5 J
(B) workdone by all forces( both real and pseudo ) in 1 sec in frame of B is 0 J
statement-B is true if the instance of starting time of movement of observer-B and the instance of force acting on the 1 kg block is same.
Psuedo force due to movement of observer-B acting on 1 kg block makes it to appear as if 1 kg block moves with
acceleration 1 m/s2 in opposite direction of movement of observer-B. Now if the 1 N force acting on block gives acceleration 1 m/s2 ,
then net result to observer B is that 1 kg block is at rest. hence workdone is zero.
If the instances of time do not coincide, 1 kg block moves with certain speed with respect to observer B due to pseudo force,
hence 1 N force acting for 1 second will not stop the block completely with respect to observer B.
Hence workdone by real force and pseudo force will not be zero.
(C) workdone by all forces( both real and pseudo ) in 1 sec in frame of C is -0.5 J - True
With respect to observer-C, 1 kg block is moving with velocity -1 m/s .
Due to action of 1 N force, 1 kg block gets acceleration 1 m/s2 .
distance S moved by block as seen by observer-C in 1 second , S = ut+(1/2)at2 = -1×1 +(1/2)×1×12 = -0.5 m
Hence workdone = force×distance = 1×(-0.5) = -0.5 J
(D) change in kinetic energy in frame-B is zero
As per the explanation given in statement-B, this statement-D is true, if the instances of staring time of observer-B and starting time of force are same.
If these instances are not same, change in kinetic energy is not zero