ISRO Scientist or Engineer Mechanical 2010

A particle is projected at an angle $$\theta$$ to the horizontal and it attains a maximum height H. The time taken by the projectile to reach the highest point, of its path is

The tension in the cable supporting a lift moving upwards is twice the tension when the lift moves downwards. Whatis the acceleration of the lift?

For the apparent weight of a body at equator to become zero, the earth should rotate with an angular velocity of

A cantilever beam AB of length L and uniform flexural rigidity EI has a bracket AC attached to its free end shown in Fig. Vertical load is applied to the free end C of the bracket. In order that the deflection of point A to be zero the ratio a/L should be

Given that
$$P_E$$ = the crippling load given by Euler
$$P_C$$ = the loadat failure due to direct compression
$$P_R$$ = the load in accordance with the Rankine’s criterion of failure
Then $$P_R$$ is given by

Bending moment M and torque is applied on a solid circular shaft. If the maximum bending stress equals to maximum shear stress developed, them M is equal to

For solid shaft subjected to a torque of 18000 Nm having a permissible shear stress of $$60N/mm^2$$, the diameter of shaft is

Shear force is

Maximum deflection in cantilever due to pure bending moment M atits end is

Maximum shear stress in Mohr’s circle is equal to