ISRO Scientist or Engineer Mechanical 2006

For the following questions answer them individually

Too high welding current in arc welding would result in

If a quantity Q is dependent on three other quantities $$q_1, q_2 and q_3$$ related such that $$Q = K \times (q_1)^{n_1} \times (q_0)^{n_2} \times (q_3)^{n_3}$$ then overall error $$\frac {\delta Q}{Q} = $$

$$\frac {PL^3}{3EI}$$ Is the deflection under the load P of a cantilever beam (length L, modulus of elasticity E, moment of inertia I). The strain energy due to bending is

A short column of external diameter D and internal diameter d carries an external load W. The greatest eccentricity which the load can have without producing tension on the cross section of the column is

A cantilever beam of negligible weight is carrying a mass at its free end, and is also resting on an elastic support of stiffness $$k_1$$ as shown in the figure below.If $$k_2$$ represents the bending stiffness of the beam, the natural frequency (rad/s) of the system is

The figure shows 3 small spheres that rotate about a vertical axis. The perpendicular distance between the axis and the center of each sphere is given. Mass of highest rotational inertia about that axis, is

A mass of 100 kg is held between two springs as shown in figure. The natural frequency of vibration of the system in cycles/second is

The bending equation is written as

If the rotating mass of a rim type flywheel is distributed on another rim type flywheel whose mean radius is half the mean radius of the former,
then energy stored in the later at the same speed will be

A thin circular disc is rolling with a uniform linear Speed, along a straight path on a plane surface. Consider the following statements in this regard:
1. All points of the disc have the same velocity
2. The center of the disc has zero acceleration
3. The center of the disc has centrifugal acceleration
4. The point on the disc making contact with the plane surface has zero acceleration
Of these statements

If a number of forces act on a rigid body, each force may be replaced by an equal and parallel force acting through a fixed point, together with a couple. For the rigid body to be in equilibrium

A fixed gear having 200 teeth is in mesh with another gear having 50 teeth. The two gears are connected by an arm. The number of turns made by the smaller gear for one revolution of arm about the center of the bigger gear is

With symbols having the usual meanings,the single degree of freedom system, $$mx + cx + kx = F \sin \omega t$$ represents

In the two - rotor system shown in the figure, $$(I_1 < I_2)$$, a node of vibration is situated

Polar moment of inertia $$(I_p)$$ of a circular disc is to be determined by suspending it by a wire and noting the frequency of oscillations (f)

Pick up the wrong statement. A flywheel

A person walks up a stalled escalator in 90 seconds. When standing on the same escalator, now moving, he is carried up in 60 seconds. How much time would it take him to walk up the moving escalator?

A stone of mass m at the end of a string of length l is whirled in a vertical circle at a constant speed. The tension in the string will be maximum when the stone is

Speed of particl e executing simple harmonic motion with amplitude a is half of the maximum speed. At that instant , displacement of the particle is

Two satellites, of masses m and 2m, are on the same circular orbit around earth. If the velocity of the lighter satellite is $$v_0$$, what is the
velocity of the heavier satellite?

If the inner and oute r surfaces of a hollow cylinder (having radii $$r_1 and r_2$$ and length L) are at temperatures $$t_1 and t_2$$ then rate of radial heat flow will be

For infinite parallel planes with emissivities $$\epsilon_1 and \epsilon_2,$$ the interchange factor for radiation from surface 1 to surface 2 is given by

The state of a real gas if changed from pressure $$P_1,$$ temperature $$T_1$$ to pressure $$P_2$$ temperature $$T_2.$$ The change in enthalpy, $$h_2 - h_1,$$ is given by

One hundredth of a kilogram of air is compressed in a piston-cylinder device. At an instant of time when T = 400 K, the rate at which work is being done on the air is 8.165 kW, and heat is being removed at a rate of 1.0 kW, the rate of temperature rise will be

The volume V versus temperature T graphs for a certain amount of a perfect gas at two pressure $$P_1 and P_2$$ are as shown in the figure. It can be concluded that

An air-conditioned room has one of the walls, which is $$5m \times 3m$$ of 3.75 cm thick brick. The conditioned space is maintained at $$27^\circ C$$ when the outside temperature is $$47^\circ C$$. Variation of thermal conductivity with temperature of the wall is given by $$k = 1 + 2 \times 10^{-4}T, where T is in degree Kelvin, and k is in $$W/m^\circ K$$. The heat gained by the conditioned space through this wall is

A mild steel tank of wall thickness 12 mm contains water at $$100^\circ C$$. The atmospheric temperature is $$20^\circ C$$. The thermal conductivity of mild steel is $$50 W/mK$$, and the heat transfer co-efficients for inside and outside the tank are 2850 and $$10 W/m^2 K$$, respectively. Calculate the rate of heat loss per $$m^2$$ of tank surface and the temperature of the outside surface of the tank.

The vector field $$\overrightarrow{F} = x\widehat{i} - y\widehat{j}$$ (where $$\widehat{i}$$ and $$\widehat{j}$$ are unit vectors) is

The transition Reynolds number for flow over a flat plate is $$5 \times 10^5.$$ What is the distance from the leading edge at which transition will occur for flow of water with a uniform velocity of 1 m/s ? (For water, the kinematic viscosity, $$\upsilon = 0.858 \times 10^{-6} m^2/s)$$

Between section 1 and 2 of a pipe a pump, a heater, a very rough pipe and an orifice plate are placed. The Bernoulli equation can be applied between 1 and 2 if

The horizontal component of force on a curved surface is equal to the

Two pipe lines at a different pressures, $$p_A$$ and $$p_B,$$ each carrying the same liquid of specific gravity $$S_1$$ are connected to a U tube with a liquid of specific gravity of $$S_2$$ resulting in the level differences $$h_1, h_2 and h_3$$ as shown in the figure. The difference in pressure head between points A and B in terms of head of water is

List I gives 4 dimensionless numbers andList II gives the types of forces, which are one of the constituents describing the numbers. Match list I with List II and select the correct answer using the codes given below the lists:

For laminar flow over a flat plate, the thickness of the boundary layer at a distance from the leading edge is found to be 5 mm. The thickness of the boundary layer at a downstream section, which is at twice the distance of the previous section from the leading edge, will be

If $$U_\infty$$ = free stream velocity, u = velocity at y, and $$\delat = boundary layer thickness, then in a boundary layer flow, the momentum thickness $$\theta$$ is given by

An automobile moving at a velocity of 40 km/hr is experiencing a wind resistance of 2kN. If the automobile is moving at a velocity of 50km/hr, the power required to overcome the wind resistance is

A cons tant-head water tank has, on one of its vertical sides two identical small orifices issuing two horizontal jets in the same vertical plane. The vertical distance between the centers of orifices is 1.5 m and the jet trajectories intersect at a point 0.5 m below the lower orifice. What is the approximate height of water level in the tank above the point of intersection trajectories?

A unit vector perpendicular to the vectors $$\overrightarrow{a} = 2i - 3j + k$$ and $$\overrightarrow{b} = i + j - 2k,$$ is

If $$\alpha, \beta, \gamma$$ are the roots of equations $$X^3 + Px^2 + qx + p = 0$$, Then the value of $$\tan^{-1} \alpha + \tan^{-1} \beta + \tan^{-1} \gamma$$ is

Solution of $$(D^2 + 16)y = \cos 4x,$$ is

Laplace transform of $$t^2 + 2t + 3$$ is

A bag contains eight white and six red marbles. The probability of drawing two marbles of same colour is

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