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Soldiers march disorderly while crossing a bridge to prevent resonance because when soldiers march in orderly manner across a bridge, they generate a rhythmic oscillation of wave on the bridge and at a certain point, would start oscillation to the same rhythm as that of the marching steps. This oscillation would reach a maximum peak when the bridge can no longer sustain its own strength and hence collapses. So for this reasons, soldier are ordered to march disorderly while crossing a bridge.

Upthrust = change in weight density = \(\frac{\text{mass}}{\text{volume}}\) Mass of liquid displaced = Density of Liquid \times Volume; = \(10^{3} \times 50 \times 10^{−6}m^{3}\) = 0.05kg (Note that the volume of \(50cm^{3}\) was converted to \(m^{3}\) by multiplying by \(10^{6}\)) i.e \(50cm^{3} = 50 \times 10^{−6}m^{3}\) Since mass displaced = 0.05kg Upthrust = mg = 0.05 \times 10 = 0.5N

Cathode rays are produced in a discharge tube under Low pressure and high voltage

For work to be done, distance must be involved because workdone = force × distance

Quantity of heat = mass(m) \times specific latent heat (L) Q = mL L = \(\frac{Q}{m}\) = \(\frac{1.13 \times 10^{6}}{15}\) = \(7.53 \times 10^{4}\)Jkg\(^{-1}\)

Internal resistance determine the maximum current that can be supplied Efficiency = \(\frac{R}{R+ r}\) \times 100 = \(\frac{6}{8}\) \times 100 = 75%

Molecules of liquid are not stationary Brownian motion is an evidence of particle nature of matter matter is made up of molecules The molecules of matter are in constant motion

Efficiency = \(\frac{ma}{V.R}\) x \(\frac{100}{1}\) V.R = number of pulleys = 6 ma = \(\frac{\text{Load}}{\text{Effort}}\) = \(\frac{200}{50}\) = 4 Effiecieny = \(\frac{4}{6}\) × 100 = 66.67%

Resistor connected in a parallel have an equivalence given by \(\frac{1}{\text{Reff}}\) = \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) = \(\frac{1 + 1 + 1}{3}\) = \(\frac{3}{3}\) = 1 Reff = 1ω

Compressor is an instrument to supply air or other gas at increased pressure Refrigerator is an appliance to keep things cold Air blower is used to release air Air conditioner is used to remove heat and maintain a stable temperature in an occupied space

Isotopy is due to difference in mass number, what causes the difference is the difference in the number of neutrons present

Moment of a force is the product of a force and the perpendicular distance from the line of action of the force Moment = force \times distance = N \times m = Nm

Magnification = \(\frac{\text{Length of camera}}{\text{distance of object from pin hole}}\) m = \(\frac{12}{60}\) = 0.2 Also magnification m = \(\frac{\text{Height of image}}{\text{Height of object}}\) ∴ Height of image = m \times height of object = 0.2 \times 70 = 14cm

H = mcθ HP = HQ, θP = 2θ, mP = \(\frac{1}{2}\)mQ ∴ HP = mQCPθP, also HQ = mQCQθQ Since HP = HQ ∴ mPcPθP = mQcPθq Putting in the conditions \(\frac{1}{2}\)mQ × cP × 2θQ = mQ × θQ × cQ ∴ cP = cQ \(\frac{C_p}{C_Q}\)= \(\frac{1}{1}\) = 1:1

The relationship between the peak value and r.m.s value of electricity supply is given as V\(_{r.m.s}\) = \(\frac{V_o}{\sqrt{2}}\) where Vo = peak voltage ∴ Vo = V\(_{r.m.s}\) × √2 = 240 × √2 = 339.5v = 340v