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Let the velocity of stream be Vs = 0.75m/s Angle at which the boat lands \theta = 30º the velocity of the boat = Vb \(\frac{0.75}{V_b}\) = Sin30º = 0.5 ∴ V\(_b\) = \(\frac{0.75}{0.5}\) = 1.5m/s

Tension = Force of gravity + acceleration force = mg + ma \(a = \frac{v - u}{t}\) = \(\frac{4 - 0}{8}\) = 0.5 ms\(^{-2}\) Tension = (\(10 \times 10) + 10 \times 0.5\) = 100 + 5 = 105N

Weight of handbag(W) = 162N acting vertically downward Angle of pull (\(\theta\)) = 60º to the vertical Since the handbag is in equilibrium, the total vertical force must equal the weight of the handbag. Let F be the force exerted by each student on the handle. The vertical component of the force from each student is given by: Fv = F cos 60º but there are two students 2Fcos60º = 162 2F(0.5) = 162 ( cos60º = 0.5) F = 162 ( since 2 x 0.5 = 1) Therefore, the force exerted by each student on the handbag is: 162N ​

LAWS OF SOLID FRICTION: Friction opposes the relative motion of two surfaces in contact. It is independent of the area of the surface of contact. It depends on the nature of the surface. It is proportional to normal reaction (R). It is independent of the relative velocity between the surfaces. Therefore, the true statements regarding sliding friction are I, II, and IV.

Water has a density of about 0.9998 g/cm³ at 0^\circC. As water is heated from 0^\circC to 4^\circC, it actually increases in density until it reaches its maximum density at approximately 4^\circC. Once the temperature exceeds 4^\circC, the density starts to decrease as the water continues to heat up towards 30^\circC. Therefore, The density will rise and fall.

The necessary conditions to produce interference fringes are I (Coherence), II (Same Frequency), and III (Same Wavelength). Condition IV (Same Intensity) is not necessary.

Refractive Index = Real Depth/App. Depth 4/3 = 6/app. depth App Depth = (3 x 6)/4 = 4.5m

When cells are connected in series, their voltages add up. However, if two cells are connected in the wrong direction, they will subtract from the total e.m.f If all cells were connected correctly, the total e.m.f. would be: Total E.M.F = 8 x 2.0V = 16V ( since no of cell = 8. and E.M.F of each cells = 2.0V) When two cells are connected in the reverse direction, their contributions effectively subtract from the total e.m.f Contribution from 2 wrongly connected cell = 2 x 2.0v = 4V Therefore, Total E.M.F = 16 - 4 = 12V.

The resultant emergent velocity of a charged ion moving through combined electric and magnetic fields can be derived from the condition where the electric force equals the magnetic force. This gives us the formula for the velocity v: q E = qvB v = \(\frac{E}{B}\) (q will cancel out) NOTE: When both fields are present, for the ion to move without deflection, the electric force must equal the magnetic force.

V = 72m U = ?, Magnification = 24 But Magnification = V/U ∴ 24 = 72/U U = 72/24 U = 3.0m

When a charged particle is accelerated across a region of p.d. V Volt, the work done is the product of the charge Q and the p.d. V i.e. Work done = Q x V But this work done is equal to the K.E. imparted to the charge given by K.E = 1/2MV2, where V is the velocity of the charge = Q x V = 1/2MV2 ∴ p.d V = (1/2MV2)/Q = 1/2 x 9.1-31 x [4 x 107]2/1.6 x 10-19 = 8 x 9.1 x 102/1.6 = 4550V = 4.55 x 103V

A cell with internal resistance can be measured accurately using a potentiometer. A potentiometer is an instrument used to measure the potential difference (voltage) across a component without drawing any current. This is crucial because drawing current can affect the measurement due to the internal resistance of the cell.

Regelation occurs when ice is subjected to pressure, causing it to melt at the point of contact. When the pressure is removed, the melted water can refreeze. This phenomenon is commonly observed in scenarios where ice is under stress, such as when a wire is pulled through it with weights attached.

1 2 3 Dry 30^\circC 29^\circC 25^\circC Wet 22^\circC 22^\circC 21^\circC Diff 8^\circC 7^\circC 4^\circC \(Relative Humidity \propto \frac{1}{temp}\) Hence, There is a steady increase in the relative humidity between Day 1 and Day 3

The vibrator is fixed at the end of the rope, hence, it is stationary. Also, the vibrator causes the end of the wire to move up and down (or side to side), creating disturbances that travel along the length of the wire. The displacement of the particles in the wire is perpendicular to the direction of wave propagation, which is characteristic of transverse waves Therefore, Option B is correct.