1.6 Two trolleys, $$ P $$ and $$ Q $$, of mass $$ M $$ and $$ 2 M $$ respectively are at rest on a frictionless horizontal surface. The trolleys have a compressed spring between them. The spring is released and the trolleys move apart. Which one of the following statements is true? (2) a) $$ P $$ and $$ Q $$ have equal kinetic energy b) The speed of $$ P $$ is less than the speed of $$ Q $$ c) The sum of the final kinetic energies of $$ P $$ and $$ Q $$ is zero d) The sum of the final momentum of $$ P $$ and $$ Q $$ is zero

Question

UpStudy AI · Accepted Answer

The problem involves conservation of momentum. Initially, the total momentum is zero because both trolleys $$P$$ (with mass $$M$$) and $$Q$$ (with mass $$2M$$) are at rest. When the spring is released, the trolleys move apart, and by the law of conservation of momentum the sum of the momenta must remain zero.

Let the speeds after release be $$v_P$$ for $$P$$ and $$v_Q$$ for $$Q$$. Conservation of momentum gives:

$$
M v_P - 2M v_Q = 0
$$

Solving for $$v_P$$:

$$
v_P = 2v_Q
$$

This shows that the total momentum remains zero (since one momentum is positive and the other negative when they move in opposite directions), which confirms that option **(d)** is correct.

Thus, the correct statement is:
 
$$
\textbf{(d) The sum of the final momentum of } P \textbf{ and } Q \textbf{ is zero.}
$$
The sum of the final momenta of trolleys $$ P $$ and $$ Q $$ is zero.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Physics Questions