Question

A boat of mass 40 kg is at rest. A dog of mass 4 kg in the boat moves with a velocity of 10 m/s. What is the velocity of the boat, nearly equals to ?
A. 4 m/s
B. 2 m/s
C. 8 m/s
D. 1m/s

Answer 1

Hint: We know that in the above question there is no external force applied on the system of boat and dog so the linear momentum will remain conserved according to the second law of newton. By equating the initial and final momentum of the boat and dog system we can easily determine the velocity of the boat.

Complete step by step solution:
According to initial data we have
Let mass of boat be $M=40kg$
Let mas of dog be $m=4kg$
Let velocity of boat with dog be $V$
Let velocity of dog be $v=10 m/s$
We know that, In the above question there is no external force applied on the system of boat and dog so the linear momentum will remain conserved according to the second law of newton.
Therefore,
Initial linear momentum = Final linear momentum
The initial momentum of the boat and dog system is zero because it is at rest.
Final momentum $= MV + mv$
On equating the initial and final momentum we get
$\Rightarrow 0 = MV + mv$
On putting the values we get
$\Rightarrow 0 = 40 \times V + 4 \times 10$
On solving we get
$V = - 1m/s$
Negative sign indicates that the velocity of the boat is in the opposite direction to that of a dog.

$\therefore$ The magnitude of velocity of the boat is 1 m/s. Hence the correct option is (D).

Note:
Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial frame it is a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics, quantum mechanics, quantum field theory, and general relativity.