91Ó°ÊÓ

The mass of block on horizontal surface is $M=4\mathrm{kg}$

The tension in the rope is $T=15\mathrm{N}$

The acceleration of the block is calculated by considering equilibrium of forces in horizontal direction.

The expression for the force is given by,

$F=ma$

Here $m$is the mass, $F$is the force and $a$is the acceleration.

(a)

Draw the diagram of the system,

The free body diagram of both the masses is are shown below,

(b)

The acceleration of the block on horizontal surface is calculated as:

$T=M{a}_x$

Here, $a_x$is the acceleration of horizontal block.

Substitute 15N for T and 4kg for M in the above equation.

$$\begin{gathered} 15N=\left(4\mathrm{kg}\right)a_x \\ {a}_x=3.75\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$

Therefore, the acceleration of either block is $3.75\mathrm{m}/{\mathrm{s}}^2$.

(c)

The mass of hanged block is calculated as:

$T=m\left(g-a_x\right)$

Here, g is the gravitational acceleration and its value is $9.8\mathrm{m}/{\mathrm{s}}^2,T$ is the tension in the moving rope.

Substitute 15N for $T,9.8\mathrm{m}/{\mathrm{s}}^2$ for g and $3.75\mathrm{m}/{\mathrm{s}}^2$for $a_x$in the above equation.

$$\begin{gathered} 15N=m\left(9.8\mathrm{m}/{\mathrm{s}}^2-3.75\mathrm{m}/{\mathrm{s}}^2\right) \\ m=2.48\mathrm{kg} \end{gathered}$$

Therefore, the mass of hanged block is 2.5 kg .

(d)

The weight of the hanged block is given as:

$$\begin{gathered} w=mg \\ w=\left(2.48\mathrm{kg}\right)\left(9.8\mathrm{m}/{\mathrm{s}}^2\right) \\ w=24.3\mathrm{N} \end{gathered}$$

The weight of the hanged block $\left(24.3\mathrm{N}\right)$ is greater than the tension$\left(15\mathrm{N}\right)$ in the rope.

Therefore, the weight of the hanging block is greater than the tension in the rope.