Question

A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the value of water
(i)displaced out of the cylinder
(ii)left in the cylinder. (Take $(\pi=\frac{22}{7})$)

Answer 1

Answer:

The volume of the water displaced out of the cylinder  is 77 cm³ and the volume of the water left in cylinder  is 748 cm³.

Step-by-step explanation:

SOLUTION :  

Given :  

Internal diameter of the cylindrical vessel = 10 cm

Radius of the cylindrical vessel , r = 10/2 = 5 cm                                    Height of the cylindrical vessel , h = 10.5 cm

Diameter of the solid cone = 7 cm

Radius of the solid cone , R = 7/2 = 3.5 cm                                                 Height of the cone , H = 6 cm

(i) Volume of water displaced out from the cylinder = Volume of the cone = V1

V1 = ⅓ × π × R² × H

V1 = ⅓ × 22/7 × 3.5² × 6

V1 =  22/7 × 3.5 × 3.5 × 2

V1 = 22 × 0.5 × 3.5 × 2

V1 = 22 × 3.5  

V1 = 77 cm³

Hence, the volume of the water displaced after immersion of the solid cone in the cylinder  is 77 cm³.

(ii) Volume of the water left in the cylinder = Volume of the cylindrical vessel – Volume of the solid cone

V = πr²h - 77

V = 22/7 × 5² × 10.5  - 77

V = 22/7 × 25 × 10.5 - 77

V = 22 × 25 × 1.5 - 77

V = 825 - 77  

V = 748 cm³

Hence, the volume of the water left in cylinder  is 748 cm³.

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Answer 2

Step-by-step explanation:

A plate of thickness t made of a material of refractive index µ is placed in front of one of the slits in a double slit experiment. (a) Find the change in the optical path due to introduction of the plate. (b) What should be the minimum thickness t which will make the intensity at the centre of the fringe pattern zero? Wavelength of the light used is λ. Neglect any absorption of light in the plate.