Exams › GATE › Technical

A circular solid shaft of span L = 5 m is fixed at one end and free at the other end. A torque T = 100 kN.m is applied at the free end. The shear modulus and polar moment of inertia of the section are denoted as G and J, respectively. The torsional rigidity GJ is 50,000 kN.m²/rad. The following are reported for this shaft: Statement i) The rotation at the free end is 0.01 rad Statement ii) The torsional strain energy is 1.0 kN.m With reference to the above statements, which of the following is true?

1. Both the statements are correct
2. Statement i) is correct, but Statement ii) is wrong
3. Statement i) is wrong, but Statement ii) is correct
4. Both the statements are wrong

Correct answer: Statement i) is correct, but Statement ii) is wrong

Solution

Statement i) is correct because the rotation at the free end can be calculated using the formula for torsion, which shows that a torque of 100 kN.m and a torsional rigidity of 50,000 kN.m²/rad results in a rotation of 0.01 rad. However, Statement ii) is incorrect as the torsional strain energy is calculated to be 2.5 kN.m, not 1.0 kN.m.

Related GATE Technical questions

• Consider a spherical globe rotating about an axis passing through its poles. There are three points P, Q, and R situated respectively on the equator, the north pole, and midway between the equator and the north pole in the northern hemisphere. Let P, Q, and R move with speeds v_P, v_Q, and v_R respectively. Which one of the following options is CORRECT?
• Muller-Breslau principle is used in analysis of structures for _____________.
• A standard penetration test (SPT) was carried out at a location by using a manually operated hammer dropping system with 50% efficiency. The recorded SPT value at a particular depth is 28. If an automatic hammer dropping system with 70% efficiency is used at the same location, the recorded SPT value will be _______.
• A vertical sheet pile wall is installed in an anisotropic soil having coefficient of horizontal permeability, k_H and coefficient of vertical permeability, k_V. In order to draw the flow net for the isotropic condition, the embedment depth of the wall should be scaled by a factor of ________, without changing the horizontal scale.
• Which one of the following options provides the correct match of the terms listed in Column-1 and Column-2? Column-1 P: Horton equation Q: Muskingum method R: Penman method Column-2 I: Precipitation II: Flood frequency III: Evapotranspiration IV: Infiltration V: Channel routing
• In the context of Municipal Solid Waste Management, ‘Haul’ in ‘Hauled Container System operated in conventional mode’ includes the _________.

⚔️ Practice GATE Technical free + battle 1v1 →