Question

113. A body of mass 4 kg is moved in a vertical plane
with sufficient speed. When the string makes an
angle 30' with the downward vertical, the tangential acceleration of the body is?​

Answer 1

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CORRECT QUESTION -

A body of mass 4 kg is moved in a vertical plane

with sufficient speed.

When the string makes an angle 30° with the downward vertical.

The tangential acceleration of the body is?

CONCEPT USED -

Rotational Motion

SOLUTION -

From the above Question , we can gather the following information...

A body of mass 4 kg is moved in a vertical plane

with sufficient speed.

We have to find the tangential acceleration of the body When the string makes an angle 30° with the downward vertical.

For the required F.B.D of the body and the depiction of the various forces acting on the body , please refer to the attachment above.

The tangencial acceleration refers to the acceleration of the body along a tangent at the point where the string breaks.

The force acting along that component is m × g × sin ( 30° )

=> 4 kg × g × ( 1 / 2 )

=> 2g

So the required tangencial acceleration of the body at that point is 2g.

ANSWER -.

The required tangencial acceleration of the body at that point is 2g.

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ADDITIONAL INFORMATION -

How to determine the X and Y components of any force acting at an angle to the horizontal $&#8658$

Suppose that a force , F is acting along an angle, $\phi$ made with the horizontal on a object.

The Horizontal Or The X component of the force :

$&#8658 \: F \cos ( \phi )$

The Vertical Or The Y component of the force :

$&#8658 \: F \sin ( \phi )$

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Answer 2

Given :-

• A body of mass 4 kg is moved in a vertical plane  with sufficient speed.

• The string makes an  angle 30° with the downward vertical.

To find :-

The tangential acceleration of the body.

Solution :-

The tangent is divided into x-component and y-component.

Tangential acceleration = g*sinθ

(The value of mass is not required here)

                                        = 9.8 * sin30°

                                        = 9.8 * 1/2

                                   = 4.9 m/s²

See the attachment.

Point to remember :-

When it comes to θ, it becomes cosθ, and when it comes to (90 - θ), it becomes sinθ.