NSMQ 2020 past questions with answers

Answer

280 J

1. 1.In an elastic collision between equal masses, the total kinetic energy is conserved: $K_{total}=K_1+K_2$.
2. 2.The struck (initially stationary) object emerges at $\theta =60^{\circ }$, so its KE is $K_1=K_{total}{\sin }^2(60^{\circ })=K_{total}\times (\sqrt{3}/2{)}^2=\frac{3}{4}{K}_{total}$. We know $K_1=840$J, so $\frac{3}{4}{K}_{total}=840⟹K_{total}=840\times \frac{4}{3}=1120$J.
3. 3.The incoming object’s KE is $K_2=K_{total}-K_1=1120-840=280$J (or directly $K_2=K_{total}{\cos }^2(60^{\circ })=1120\times \frac{1}{4}=280$J).

Answer

Electrolysis of molten $\text{NaCl}$ to produce sodium metal and chlorine gas.

1. 1.A Downs cell is an electrolytic cell designed to decompose molten $\text{NaCl}$.
2. 2.At the cathode sodium ions are reduced: ${\text{Na}}^{+}+e^{-}\to \text{Na}(l)$.
3. 3.At the anode chloride ions are oxidised: $2{\text{Cl}}^{-}\to {\text{Cl}}_2(g)+2e^{-}$; molten conditions and separation prevent recombination or water reduction.
4. 4.Therefore the Downs cell carries out the electrolysis of molten $\text{NaCl}$ to give sodium metal and chlorine gas.

Answer

$(1-2x)/(3x-2)$

1. 1.Let y = f(x) = (2x + 1)/(3x + 2).
2. 2.Swap x and y to get x = (2y + 1)/(3y + 2), then multiply both sides by (3y + 2): x(3y + 2) = 2y + 1.
3. 3.Distribute and collect y terms: 3xy + 2x = 2y + 1 → 3xy − 2y = 1 − 2x → y(3x − 2) = 1 − 2x → y = (1 − 2x)/(3x − 2).

Answer

A = 2, B = −1

1. 1.Assume the decomposition $\frac{x+7}{(x-3)(x+2)}=\frac{A}{x-3}+\frac{B}{x+2}$.
2. 2.Multiply both sides by $(x-3)(x+2)$ to clear denominators: $x+7=A(x+2)+B(x-3)$.
3. 3.Substitute $x=3$ to get $3+7=A(5)⟹A=2$.
4. 4.Substitute $x=-2$ to get $-2+7=B(-5)⟹B=-1$.

Answer

70 mW

1. 1.Write the laser output relation: $P_{out}=\eta (P_{pump}-P_{th})$.
2. 2.Substitute the given values: $10\mathrm{mW}=0.2(P_{pump}-20\mathrm{mW})$.
3. 3.Divide both sides by 0.2 to get $P_{pump}-20=50$, then add 20 to find $P_{pump}=70\mathrm{mW}$.

Answer

mol⁻¹ dm³ s⁻¹

1. 1.Write the rate law for a second-order reaction: $r=k[A{]}^2$.
2. 2.Identify units: rate $r$ has units mol dm⁻³ s⁻¹; concentration $[A]$ has units mol dm⁻³.
3. 3.Solve for $k$: $k=\frac{r}{[A{]}^2}$ so unit$(k)=\frac{{\text{mol\hspace{0.17em}dm}}^{-3}{\text{s}}^{-1}}{({\text{mol\hspace{0.17em}dm}}^{-3}{)}^2}={\text{mol}}^{-1}{\text{dm}}^3{\text{s}}^{-1}$.

Answer

False

Because v_e = √(2GM/R), escape velocity depends on the square root of mass and the radius, not linearly on mass.

Answer

True

Ions like K+ affect osmotic balance.

Answer

Axon

Answer

73