Question

A dog weighing 5kg is standing on a flat boat so that it is 10 metres from the shore. It walks 4m on the boat towards the shore and then halts. The boat weighs 20kg and one can assume that there is no friction between it and water. The dog from the shore at the end of this time is:

• A. 3.4 m
• B. 6.8m
• C. 12.6 m
• D. 10m

Answer 1

The correct option is B 6.8m

The correct answer is B.

GIven,

Mass of dog is $5kg$,

Mass of the boat is $20kg$

$x_1$ is the distance of the center of mass of boat from the shore, and $x_c$ is the distance of the center of mass of the system from the shore.

$X_{cm}=\frac{5\times 10+20\times 1}{20+5}$

=$2+\frac{4}{5}\times 1$

Now, let boat move x distance away from the shore when a dog moves 4m towards the shore

.

So, the distance of boat from shore=$x_1+x$

Now, the distance of dog from shore =$10-4+x$

=$6+x$

Now,

$x_{cm}=\frac{5\times (6+x)+20\times (x_1+x)}{20+5}$

=$\frac{30+25x+20x_1}{25}$

equating both $x_{cm}$

$\frac{6}{5}+x_1+\frac{4}{5}=2+\frac{4}{5}$

so,

distance$=6+\frac{4}{5}=\frac{34}{5}m$

=$6.8m$