Ans. 20kg, 0.5m and 1sec.

Sol. Let M 1 , L 1 and T 1 be the units of mass, length and time in SI and M 2 , L 2 and T 2 the corresponding units in new system.

The dimensional formula for force is (M 1 L 1 T –2 )

Hence the conversion formula for force becomes

n 2 = n 1

Here n 1 = 10N, n 2 = 1, Substituting we get

1 = 10 …….(1)

The dimensional formula for work is (M 1 L 2 T –2 )

n 2 = n 1

n 1 = 5J, n 2 = 1

Substituting values we get

1 = 5 ...…(2)

Similarly dimensional formula for velocity is (MºL 1 T –1 ).

Hence, conversion formula for velocity is

n 2 = n 1

Here, n 1 = 0.5 ms –1 , n 2 = 1,

Substituting values we get

1 = 0.5 …….(3)

Dividing (2) by (1), 1 = , L 2

= = m = 0.5

Substituting value of in (3), we get

1 = 0.5 × 2 , = 1, T 2 = 1s

Substituting value of and in (1)

1 = 10 × 2 × 1,

1 = 20 ,

M 2 = 20 M 1 as M 1 = 1 kg, M 2 =20 kg.

Hence unit of mass, length and time are 20kg, 0.5m and 1sec. respectively.