Hearty Wallows

Fuel supplied to an SI engine has a calorific value 42000 kJ/kg. The pressure in the cylinder at 30% and 70% of the compression stroke are 1.3 bar and 2.6 bar respectively.Assuming that the compression follows the law pV^1.3 = constant .Find the compression ratio.

A four cylinder SI engine running at 1200 rpm gives 18.87kW as brake power.When one cylinder missed firing the average torque was 100 Nm. Calculate the indicated thermal efficiency if the CV of fuel is 42 MJ/kg.The engine uses 0.335 kg of fuel per kW/h.What is mechanical efficiency?

Is there an analytic function f(z) = u +iv for which v = e^(y/x)?

Please explain your answers in detail

(∂^2/∂x^2 + ∂^2/∂y^2).log |f ' (z) | = 0

Hint :

z = x + iy

f(z) = u + iv

f ' (z) = ∂u/∂x + i∂v/∂x

and

∂u/∂x = ∂v/∂y

∂v/∂x = - ∂u/∂y

∂^2u/∂x^2 + ∂^2u/∂y^2 = 0

∂^2v/∂x^2 + ∂^2v/∂y^2 = 0

Show that the curves r^n = a.sec(n@) and r^n = b.cosec(n@) intersect orthogonally.

1. A uniform sphere of weight W rests between a smooth vertical plane and a smooth plane inclined at an angle @ with the vertical plane. Find the reaction at the contact surfaces.

2.A spherical ball of weight 50 N is suspended vertically by a string 500 mm long. Find the magnitude and direction of the least force, which can hold the ball 100 mm above the lowest point.Also find tension in the string at that point.

1. A beam AB 5m long is supported at its ends A and B .Two point loads W1 and W2 are placed at C and D , 1m and 3m respectively from the end A . If the reaction at A is twice the reaction at B , find the ratio of load W1 and W2.

Answer is 2: 1, but I don't know how to arrive at it

2.A tricycle weighing 200N has a small wheel symmetrically placed 500 mm in front of two large wheels which are placed 400 mm apart .If the centre of gravity of the cycle be at a horizontal distance of 150 mm from the rear wheels and that of the rider , whose weight is 150 N , be 100 mm from the rear wheels , find the thrust on the ground under the different wheels.

Answer is 90N; 130N; 130N but I don't know how to arrive at it

3.An oil drum of 500mm diameter and 1.5m long is to be rolled across a footstep of 100 mm high.Find the minimum push required at the top of the drum.Take density of the oil as 1kg/litre .Neglect weight of the drum.

Answer is 1444.5 N

If I is the intensity of principal maximum in the single slit diffraction pattern ,then what will be its intensity when slit width is doubled?

1. I * Pi/w [( w- omega)]

2. I/2

3. 2I

4. 4I

answer is 2I but i dunno the approach.Kindly explain whatever your answer may be!!Thanks!!

Diameter of hyperbola i guess .but dunno the equation

Q4.A variable chord PQ of the parabola , y^2 = 4x is drawn parallel to the line y = x .If the parameters of the points P and Q on the parabola be p and q respectively , then (p+q) =

A. 1

B 0.5

C. 2

D. 4

Please explain Your answers

Q3.Two perpendicular chords are drawn from the origin 'O' to the parabola y = x^2 , which meet the parabola at P and Q .Rectangle POQR is completed . Find the locus of vertex of R.

Q2.If normal of the circle x^2 + y^2 +6x +8y +9 =0 intersect the parabola y^2 = 4x at P and Q then find the locus of point of intersection of tangent's at P and Q

Q1.If a line x +y =1 cut the parabola y^2 = 4ax in the points A and B and normals drawn at A and B meet at C. The normal to the parabola from C ,other than above two meet the parabola in D, then find D

Find the co - ordinates of the two points Q and R , where the tangent to the hyperbola x^2/45 - y^2/20 = 1 at the point (9,4) intersects the two asymptotes

Given the base of a triangle and the ratio of the tangent of half the base angles .Show that the vertex moves on a hyperbola whose foci are the extremities of a diameter

Prove that the tangent to a hyperbola makes with the asymptotes a triangle of constant area and the portion of the tangent is bisected at the point of contact

If a circle be drawn so as always to touch a given straight line and also a given circle externally then prove that the locus of its centre is a parabola .(given line and given circle are non intersecting )