Motion of Connected Bodies

Practice Questions:

Question 1: easy

Three blocks A, B and C of masses 4 kg, 2 kg and 1 kg respectively, are in contact on a frictionless surface, as shown. If a force of 14 N is
applied on the 4 kg block, then the contact force between A and B is

connected body nlm

1. 18 N

2. 2 N

3. 8 N

4. 6 N

View Answer

The total mass of the system:

$M = 4 + 2 + 1 = 7 \text{ kg}$

The acceleration of the system:

$a = \frac{\text{Total Force}}{\text{Total Mass}} = \frac{14}{7} = 2 \text{ m/s}^2$

Now, considering block B and C together (mass =

$2 + 1 = 3$

kg), the force required to accelerate them:

$F_{AB} = (3 \times 2) = 6 \text{ N}$

Thus, the contact force between A and B is 6 N.

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Question 2: easy

A spring of length $L$ and spring constant $K$ is cut into two parts of length $\frac{L}{3}$ and $\frac{2L}{3}$, then the spring constant of each part will be

1. $3K, \frac{3K}{2}$

2. $2K, \frac{2K}{3}$

3. $K, \frac{K}{3}$

4. $K, K$

View Answer

The spring constant is inversely proportional to the length of the spring: $k \propto 1/l$. For lengths $L_1 = L/3$ and $L_2 = 2L/3$, the spring constants are $k_1 = 3K$ and $k_2 = 1.5K = 3K/2$.

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