Question

You and your friend are travelling on a spacecraft which moves with respect to the stars at close to the speed of light. Compared to the situation when you were both on Earth, you will observe the following;
a) Your friend's mass would increase.
b) Your friend's heart rate will increase.
c) Both (a) and (b) will happen simultaneously.
d) Neither (a) nor (b) will happen.

Answer 1

c) is correct I believe, as you travel near the speed of light, time slows down and you become heavier

Answer 2

d

Answer 3

b) Your friend's heart rate will increase

Mass cant increase or decrease............its weight which can be increase or decrease
depending on gravitational pull.

If you are traveling with speed of light then world will be appear to be slow down to you or
you are so fast that everything is slow. so heart rate should increase if u count it with considering time on earth.

Answer 4

Yes the invariant mass can not change in a close system. However the relative mass, compared in at least 2 different time frames can. Since we're talking about 2 frames of reference, Earth and the spaceship travelling near lightspeed, the "mass" relative to each time frame is thus different.

(The term relativistic mass is also sometimes used. This is the sum total quantity of energy in a body or system (divided by c2). As seen from the center of momentum frame, the relativistic mass is also the invariant mass, as discussed above (just as the relativistic energy of a single particle is the same as its rest energy, when seen from its rest frame). For other frames, the relativistic mass (of a body or system of bodies) includes a contribution from the "net" kinetic energy of the body (the kinetic energy of the center of mass of the body), and is larger the faster the body moves. Thus, unlike the invariant mass, the relativistic mass depends on the observer's frame of reference. However, for given single frames of reference and for closed systems, the relativistic mass is also a conserved quantity) - Wikipedia