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The unit of a couple is Newton-meter (N M)

Wt in the air = 250N wt. in the liquid = 200N loss in wt. in the liquid = 250 - 200 = 50N ∴ mass of liquid displaced = 50N → 5kg ∴If the density of the liquid is 1000kgm-3 then the volume of the liquid = (M)/D = V = (5kg)/1000 = 0.005 → 5.0 X \(10^{-3}\)\(m^3\)

Electricity heat energy supplies by the heater = lvt = 3.5 x 200 x (2 x 60) = 84000j. and this heat is supplied to the 2 kg of the water MC ∆ t = 84000 2 x 4200 x ∆ t = 84000 ∴ ∆t = (84000)/8400 = 10°c ∴ increase in temp. of water = 10°c

Increase in pressure generally raises the boiling point but but lowers the melting point. II and III

Diffusion rates of a substance generally depend on mass, density, and temperature. and nature of substances I II, III, and IV

E = HF = (hc)/\lambda E\lambda = hc ∴ X = hc ==6.63 x 10\(^{-34}\) x 10\(^8\) = 1.989 x 10\(^{-25}\) =1.99 x 10\(^{-25}\)

Resolution of force: Total vertical upward force: = 3√3 + 10 cos 60o = 3√3 + 5. Total downward force = 6 cos 30o = 6 x √(3/2) = 3√3 Total horizontal forces towards right; = 3N + cos 30o = 3N + 10 x √(3/2) = 3N + 5√3 Total horizontal forces towards left: = 6 cos 60o = 6 x 0.5 = 3.0N Summary: Vertical resultant forces upward: = 3√3 + 5 - 3√3 = 5N Horizontal resultant forces towards right: = 3N + 5√3 - 3√3 = 5N Horizontal resultant force towards right = 3N + 5√3 - 3N = 5√3N ∴ R2 = 52 + (5√3)2 = 25 + 25 x 3 = 100 ∴ R = √100 = 10N

The ball has its fastest speed at its equilibrium position when its displacement X = 0, which is at X. At this point, the bob has maximum velocity and maximum kinetic energy.

Being a uniform rod, the height W should be acting at the mid point 25cm mark. ∴ Taking moment about the fulcrum, F, 200 x 10 = W x 10 + 40 x 30 2000 = 10W + 1200 => 10W = 2000 - 1200 = 800 w = 800/10 = 80N

Effective component of the force along the horizontal = F cos 60o Work done by this force : 60 F cos 60 x X = 2 x 0.5 x 3 = 3J

Use Fleming's Left-Hand Rule to find the direction: First Finger (Field): Point it into the paper/screen. Thumb (Force): Point it upwards. Second Finger (Current): It will naturally point to the right.

From faradays law, M = itz But mass, M = volume x density and volume = cross-sectional area x thickness M = 118.8 x 10\(^{-6}\) x 9 x 10\(^3\) ∴ 118.8cm2 x 10\(^{-6}\) x 9 x 10\(^3\) = 10 x t x 3.3 x 10\(^{-7}\) ∴ (118.8 x 9) x 10\(^{-7}\) = 10 x t x 3.3 x 10\(^{-7}\) ∴ t = \(\frac{118.8 \times 9}{ 3.3}\) t = 324 seconds Convert to minutes by dividing by 60 t = \(\frac{324}{60}\) t = 5.4 mins.

\(V_T = 5m^3, m_1 = 2 \times 1 \times 10^3 = 2 \times 10^3\) \(M_2 = 3 \times 8 \times 10^3 = 24 \times 10^3\) MT = 26 x 103 D = \(\frac{m}{v} = \frac{26 \times 10^3}{5} = 5.2 \times 10^3\)

No expanded working has been attached for this question yet. The verified answer is Option A.

The forces acting on the mass include: Weight: W = mg (downward) Upthrust: U (upward) Viscous Drag: F (upward) Since the mass is descending at a steady velocity, the net force acting on it is zero. This means that the upward forces (upthrust and viscous drag) balance the downward force (weight): mg = U + F = U + F - mg = 0