★ Given :-

• An object rolls down along an incline that rises by 3 on every 5(along it).
• The object gains a speed of √10m/s as it travels a distance of 5/3m along the incline.

★ Have to Find :-

What can be the possible shapes of object?

★ Solution :-

Now, from given we know that sin (theta) will be 3/5.

From given we know, the object covers linear distance which is equal to :-

s →

Therefore, substituting the values to get the height.

s × sin θ = h

" s " = 5/3

" sinθ " = 3/5

Now, we are going to use the formula velocity of the object in order to find the k²/R²

So, we know the formula ,

Velocity → √2gh / ( 1 + k²/ r² )

" g " → 10

" v " → √ 10m/s

" h " → 1

Simply substituting the values :-

√ 10 = √2gh / ( 1 + k²/ r² )

Root cancels root

➹ 10 = 2 * 10 * 1 / 1 + k²/R²

➹ 10/10 = 2 * 1 / 1 + k²/ R²

➹ 2 * 1 = 1 + k²/ R²

➹ 2 = 1 + k²/ R²

Transposing 1

2 - 1 =   1 + k²/R²

    1 =  k² /R²

Hence,

The object is either ring or hollow cylinder.

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Verified answer

✏️ Answer:-

★ The possible shapes of the object must be a ring or hollow cylinder.

✏️ Explanation:-

★ Given:-

• Incline that rises by 3 in every 5 -- (will be) sin θ = 3/5

• Object gains a speed , v = √10 m/s

• Traverses a distance along the incline, s = 5/3

• Value of g = 10 m/s²

★ To find:-

• Probable shape/s of the object... i.e., to acquire the ratio of K²/R² which will

be further determining the possible rolling object.

★ Solution:-

• From the given scenario, we have,

Sin θ = 3/5

And the linear distance traversed by the object along the plane, s = h/sin θ.

⇒h = s

⇒sin θ = 5/3 × 3/5 = 1

Now, as we know,

The velocity of any rolling body is given by,

Thus,

On plugging in the respective values and comparing the above expression, we get,

Therefore,

We can conclude that the given object must either be a ring or a hollow cylinder.

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I hope this helps! :)