Correct answer is (A)

Here given that

density of a material in SI units is 128 kg m^–3

And a new unit system is introduced where 1 unit of length = 25 cm and 1 unit of mass = 50 g

You should know that, physical quantity is same in any unit system. And to calculate a physical quantity yo should know two things

(1) numerical value of the physical quantity (n)

(2) unit of the physical quantity (u)

And n $\times$ u = constant in any unit system.

Here in SI unit system,

n₁ = 128

u₁ = kg/m³

And in new unit system,

n₂ = ?

u₂ = 50gm/(25cm)³

As n₁u₁ = n₂u₂

$\therefore$ 128 $\times$ (kg/m³) = n₂ $\times$ 50gm/(25cm)³

$\Rightarrow$ 128 $\times$ $\frac{1000gm}{{\left(100cm\right)}^3}$ = n₂ $\times$ $\frac{50gm}{{\left(25cm\right)}^3}$

$\Rightarrow$ n₂ = 128 $\times$ $\frac{20}{4^3}$ = 40

Correct answer is (A)

23.023 has 5 significant figures.

0.0003 has 1 significant figure.

2.1 $\times$ 10^–3 has 2 significant figures.

Correct answer is (A)

Momentum, p = m $\times$ v

= 3.513 $\times$ 5.00 = 17.565 kg m/s

$\simeq$ 17.6 kg m/s

Here number of significant digits in m is 4 and in v is 3, so, p must have minimum (which is 3) significant digit.

Note :

In this case, since we are calculating the magnitude of momentum, which is given by the absolute value of the product of mass and velocity, we should follow the rules for significant figures as if we were multiplying the two values together.

The least precise value in the calculation has three significant figures (the velocity), so we should round the answer to three significant figures as well.

Therefore, the correct answer with three significant figures is 17.6 kg m/s.