Question

A metal bar of mass 3.6 kg is cut into two pieces in the ratio 3:5. The length of the shorter piece is 45 cm. Find :

(a) the length of the longer piece,

(b) the length of the original metal bar,

(c) the mass per unit length of the bar in kg/m

(d) the mass of the shorter piece​

Answer 1

Answer:

I am not sure of the c and d but

a is 75cm

b = 120 cm

Step-by-step explanation:

A

3 units = 45cm

1 unit = 45/3 = 15

5 units = 15 * 5 = 75cm

B

75 + 45 = 120

Answer 2

Given:

• Mass of metal bar = 3.6 kg
• The ratio in which the metal bar was cut = 3:5
• Length of the shorter piece = 45 cm

To find:

1. The length of the longer piece
2. The length of the original metal bar
3. Mass per unit length of the bar in kg/m
4. Mass of the shorter piece

Solution:

1. Let the length of the longer piece = x

                         $\frac{3}{5} = \frac{45}{x}$

           3x = 45 * 5

           3x = 225

             x = $\frac{225}{3}$ = 75 cm

Thus the length of the longer piece is 75 cm.

2. Length of original metal bar = Length of the shorter piece + Length of the longer piece

Length of the original metal bar = 45cm + 75 cm = 120 cm

Thus the length of the original metal bar is 120 cm.

3.  Mass per unit length = $\frac{Total mass}{Total length}$

Mass per unit length = $\frac{3.6 kg}{1.2 m}$ = 3kg/m                 ( 120cm = 1.2 m)

Thus mass per unit length of the metal bar is 3kg/m.

4. Mass of shorter piece = Mass per unit length x Length of the shorter piece

Mass of shorter piece = 3kg/m x 0.45m = 1.35 kg

Thus the mass of the shorter piece is 1.35 kg.