According to principle of conservation of energy, the total momentum of a system of masses in any direction remains constant unless acted upon by an external force in that direction. A. True B. False

False on two counts:

1. It is law of conservation of momentum and not energy.

2. The word total momentum means the sum of momentums, used by you is not correct because it denotes momentum as scalar and adds up momentums in different directions like x, y, z etc i.e.

p = m_x + my + m_{z [Note physical quantity momentum is symbolized as p]}

Whereas Momentum is a vector and hence net momentum remains constant in the absence of external force. Momentum in different directions add up vectorially. The force, F = dp/dt (bold letter means vector). That is F = dpx/dt + dpy/dt + dpz/dt.

In the absence of external force, F = 0; therefore dp/dt = 0 ⇒p = constant where p = p_x + p_y + pz.

False on two counts:

1. It is law of conservation of momentum and not energy.

2. The word total momentum means the sum of momentums, used by you is not correct because it denotes momentum as scalar and adds up momentums in different directions like x, y, z etc i.e.

p = m_x + my + m_{z [Note physical quantity momentum is symbolized as p]}

Whereas Momentum is a vector and hence net momentum remains constant in the absence of external force. Momentum in different directions add up vectorially. The force, F = dp/dt (bold letter means vector). That is F = dpx/dt + dpy/dt + dpz/dt.

In the absence of external force, F = 0; therefore dp/dt = 0 ⇒p = constant where p = p_x + p_y + pz.

No.

It is due to CONSERVATION OF MOMENTUM and not conservation of energy. 

Extra Info - In higher classes when you will read about four-vectors (hence four-velocity, four-momentum etc) the law of conservation of emeren and law of conservation of momentum will be combined into one as law conservation of four-momentum.