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The velocity, V, for the stream-line flow of a liquid in a small uniform tube depends on the radius, r, of the tube, the density, ρ, and the coefficient of viscosity, η, of the liquid. Use the method of dimensional analysis to obtain an expression for velocity. (5)
2. Show whether or not the following have similar dimensions:
(a) Young’s modulus and Stress (3) (b) Force and Power (3)
3. The position of a particle moving along the x-axis is given by x = 7t2 + 2t3, where x is in meters and t is in seconds. Determine the following, when t = 1.4 s:
(a) The position (2) (b) The velocity (2) (c) The acceleration (2)
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4. Letvectors 𝑨=𝑛𝑖̅−3𝑗̅+2𝑘 and𝑩 =3𝑖̅−2𝑗̅+3𝑘
(a) Find the scalar product of the two vectors. (3) (b) For n = 3, find the cross product of the two vectors. (4) (c) For n = 1, use the cross product to find the angle between the two vectors. (6)
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5. A vector 𝑹 has a direction of 30 with respect to the y-axis. Draw this vector and find
its x and y components if its magnitude is 7 m.
G=GMm/r² where f is magnitude of the force m and m are the sizes of each mass r is the distance between the masses and G is a constant if both M and r are halved keeping all other values constant what is the ratio of the new force F1 to the original force f0 (F1/f0
In Newton’s rings experiment using light of two wavelengths , it is observed that 10 th order bright ring corresponding to wavelength 1 coincides with 15 th order dark ring corresponding to wavelength λ₂ when viewed by reflected light. Find the ratio of λ1 and λ₂
b) Find the power delivered to an element at t = 3 ms if the current entering its positive terminal is i = 5cos60πt A and the voltage is
(i) v = 3i
(ii) v = 3di/dt
3. The electric (E) and magnetic (H) field vectors in a medium are given by
𝑬 = 𝒊^ 20𝑐𝑜𝑠(𝜔𝑡 + 𝜋𝑦)𝑉/𝑚 , 𝑯 = 𝒌^ 20 𝑐𝑜𝑠(𝜔𝑡 + 𝜋𝑦)𝐴/𝑚
𝜂
Use Maxwell’s equations to determine η and ω. Assuming that for the medium 𝜀 = 36𝜀𝑜 ,
𝜇 = 𝜇𝑜 .
Two balls A and B, weighing 49 N each, approach each other, with speeds of 20 m/s and 30 m/s respectively. Determine their speeds after the collision if (a) the coefficient of restitution is 0.80, and (b) they are completely inelastic.
Three resistors with values of 60.0Ω, 30.0 Ω, and 20.0 Ω, respectively, are
connected in series to a 110.0 V battery of negligible internal resistance. (a) Draw a circuit diagram and find the (b) equivalent resistance of the combined resistors, (c) current flowing through each resistor, (d) voltage drop across each resistor.
A certain resistance thermometer reads 14.5 Ω in pure melting ice and 18.5 Ω in steam at standard atmospheric pressure. What will be its resistance at room temperature of 27.0oC?
A body of mass 0.6kg is thrown vertically upward from ground with a speed of 20ms-1. Calculate its potential energy at the maximum height
a mechanical oscilator has initial energy Enot= 50j having a damping coefficient b=1s. Calculate the time required to decrease to E= Enot/e
#339914 on Dec 2023