3. 4. 5. When a tension force T is applied to a spring the extension x is related to T by Hooke law, T=kx where k is called the stiffness of the spring. What is the dimension of k? for the period of oscillation of mass m Verify the correctness of the formula t = 2π suspended by a spring of stiffness k. (6) 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 p and the coefficient of viscosity 17 of the liquid. Use the method of dimensional analysis to obtain an expression for the velocity V. and use your result to obtain the value of the constant K if V. where is the length of liquid. (6) p. 4nl Two vectors are given by A-3i+4j and Bi+3j+6k, Find (i) AxB (4) 49€ (ii) the angle between A and B by cross product. (iii) the scalar product of the two vectors A and B. 6. If vectors a-b= 2c, a+b=4c and c=31+ 4j, Find a and b. (4) 7. The position of an object is given by 1.03 -7.0 tj+ 3.0 tk. m (with t in seconds). Determine; (i) (ii) an expression for the rate of change of displacement of the particle; the magnitude of the velocity when the time is 7.0 seconds; (3) (iii) the unit vector ñ in the direction of the acceleration when time t is 2.0 seconds; (6)
