We are given a situation where an object of weight 25 kg is placed on a smooth plane inclined at 30° to the horizontal. We are asked to find two things:

Given Data:

• Mass of the object: $m = 25 \, \text{kg}$
• Angle of the incline: $\theta = 30^\circ$
• Gravitational acceleration: $g = 10 \, \text{m/s}^2$

Part (a): Acceleration of the object as it moves down the plane

On an inclined plane, the force causing the object to move down the incline is the component of the gravitational force parallel to the incline. This force is given by:

$F_{\text{parallel}} = mg \sin \theta$

The acceleration of the object $a$ can be found using Newton's second law:

$a = \frac{F_{\text{parallel}}}{m} = g \sin \theta$

Substituting the values:

$a = 10 \times \sin 30^\circ$

Since $\sin 30^\circ = 0.5$:

$a = 10 \times 0.5 = 5 \, \text{m/s}^2$

So, the acceleration of the object is $5 \, \text{m/s}^2$.

Part (b): Velocity attained after 5 seconds if it moves with an initial velocity of 10 m/s

We use the equation of motion:

$v = u + at$

Where:

• $v$ is the final velocity
• $u = 10 \, \text{m/s}$ is the initial velocity
• $a = 5 \, \text{m/s}^2$ is the acceleration
• $t = 5 \, \text{seconds}$ is the time

Substituting the values:

$v = 10 + 5 \times 5 = 10 + 25 = 35 \, \text{m/s}$

So, the velocity attained after 5 seconds is $35 \, \text{m/s}$.

Final answers:

• (a) Acceleration of the object: $5 \, \text{m/s}^2$
• (b) Velocity after 5 seconds: $35 \, \text{m/s}$

Would you like further clarification or more details on any part? Here are some related questions you might find helpful:

1. What is the effect of the incline angle on the acceleration?
2. How would the presence of friction change the calculation?
3. How can we find the distance traveled by the object in 5 seconds?
4. What would happen if the plane was vertical (i.e., at $90^\circ$)?
5. How does the object's mass affect the acceleration on a smooth incline?

Tip: The acceleration on an inclined plane depends only on the angle and gravity, not the mass of the object.