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Given : differential equation
\(\left [ 1+\left ( \frac{d^{3}y}{dx^{3}} \right )^{2} \right ]^{4/3}= \frac{d^{2}y}{dx^{2}}\)
Order and degree of the differential equation are
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Residue of 8z cos1⁄z at z= 0 is _______.
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The directional derivative of f (x, y, z) = x2 + y2+ z2 at the point (1, 1, 1) in the direction \(\hat{i}-\hat{k}\) is _______.
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Nullity of the matrix A=\(\begin{bmatrix} -1 &4 &2 \\ 1 &3 &2 \\ -2 &1 &0 \\ 2&6 & 4 \end{bmatrix}\) is _____________ .
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Two coil springs, each having stiffness K, are placed in parallel. The stiffness of the combination will be :
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Solution
Given:k1= k2= k,
where the springs are in parallel,K(equivalent)= K1+ K2= k+ k = 2k
A square key of side d/4 is to be filled on a shaft of diameter d and in the hub of a pully. If the material of key and shaft is same and the two are equally strong in shear,then the length of key is:
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A reciprocating engine, running at 80 rad/s is supported on springs. The static deflection of spring is 1 mm. g =10 m/s2. When the engine runs, the frequency of vibrations of the system is ………………..
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The value of radius of gyration of disc type flywheel as compared to rim type flywheel for the same diameter is:
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Solution
For disc type flywheel
Radius of gyration (k) =r/√2
where, r = radius of disc
For rim type flywheel,
Radius of gyration (k) = r.
The relative jet exit velocity from a rocket is 2700 m/s. The forward flight velocity is 1350 m/s. The propulsive efficiency of the unit is ………………..
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