Question

Two blocks of mass M and m, are used to compress two different massless springs as shown in the figure. The left spring is compressed by $3\text{cm}$, while the right spring is compressed by an unknown amount. The system is at rest and all contact surfaces are smooth. Which of the following statements are true?

• A. The force exerted on block of mass m by the right spring is 6 N to the left.
• B. The force exerted on block of mass m by the right spring is impossible to determine.
• C. The net force on block of mass m is zero.
• D. The normal force exerted by block of mass m on block of mass M is 6 N.

Answer 1

Answer: (A), (C), (D)

The correct options are
A The force exerted on block of mass m by the right spring is 6 N to the left.
C The net force on block of mass m is zero.
D The normal force exerted by block of mass m on block of mass M is 6 N.

Let F be the force exerted by mass m on mass M.
FBD of mass M

$F=k_1{x}_1=2\times 3$
$=6\text{N}$
FBD of mass m

$k_2{x}_2=F=6\text{N}$ to the left
Hence the force exerted on block of mass m by the right spring $\left(k_2{x}_2\right)$ is 6 N to the left. From FBD, the normal reaction (F) between blocks is 6 N.
As system is at rest, net force on block of mass m is zero.