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51.	A block of weight Q rests on an inclined plane and it is attached to a string which runs over a frictionless pulley to carry a block of weight P at its other end. The coefficient of friction between the block of weight Q and the inclined plane is μconsider the following cases:Case -I: weightQ starts moving down the inclined planeCase -II: weight P starts falling downThe limiting values of ratio P/Qfor case I and case II respectively are
Answer» A block of weight Q rests on an inclined plane and it is attached to a string which runs over a frictionless pulley to carry a block of weight $P$ at its other end. The coefficient of friction between the block of weight Q and the inclined plane is $μ$ consider the following cases: Case -I: weightQ starts moving down the inclined plane Case -II: weight P starts falling down The limiting values of ratio $P / Q$ for case I and case II respectively are

52.	The rectilinear motion of a particular is defined by the displacement time equationx = x0[2e−kt−e−2kt]Where x0 is the initial displacement, K is a constant. What will be the maximum velocity of the particle?
Answer» The rectilinear motion of a particular is defined by the displacement time equation x = $x_{0} [2 e^{- k t} - e - 2 k t]$ Where $x_{0}$ is the initial displacement, K is a constant. What will be the maximum velocity of the particle?

53.	Consider a truss ABC loaded at C as shown in figure. Which of the following options is correct.
Answer» Consider a truss $A B C$ loaded at $C$ as shown in figure. Which of the following options is correct.

54.	For the truss shown in figure, the magnitude of the force in member PR and the support reaction at R are respectively
Answer» For the truss shown in figure, the magnitude of the force in member PR and the support reaction at R are respectively

55.	A uniform rigid rod of mass M and length L is hinged at one end as shown in the adjacent figure. A force P is applied at a distance of 2L3 from the hinge so that the rod swings to the right. The horizontal reaction at the hinge is
Answer» A uniform rigid rod of mass M and length L is hinged at one end as shown in the adjacent figure. A force P is applied at a distance of $\frac{2 L}{3}$ from the hinge so that the rod swings to the right. The horizontal reaction at the hinge is

56.	For the same material and the mass, which of the following configurations, of flywheel will have maximum mass moment of inertia about the axis of rotation OO' passing through the center of gravity.
Answer» For the same material and the mass, which of the following configurations, of flywheel will have maximum mass moment of inertia about the axis of rotation OO' passing through the center of gravity.

57.	At the instant shown in figure, 0.4 kg slender rod has an angular velocity of 6.9 rad/s and is subjected to force F=6.6N and moment M=59N−m. If the rod length ∠=4 m, what will be the angular velocity of the rod when it is rotated by 90∘ downwards?(Assuming the force is always perpendicularto the axis of the rod. g=9.81 m/s2)
Answer» At the instant shown in figure, 0.4 kg slender rod has an angular velocity of 6.9 rad/s and is subjected to force $F = 6.6 N$ and moment $M = 59 N - m$ . If the rod length $∠ = 4 m$ , what will be the angular velocity of the rod when it is rotated by $90^{\circ}$ downwards? (Assuming the force is always perpendicularto the axis of the rod. $g = 9.81 m / s^{2}$ )

58.	A force F is acting on a bent bar which is clamped at one end as shown in the figure.The CORRECT free body diagram is
Answer» A force F is acting on a bent bar which is clamped at one end as shown in the figure. The CORRECT free body diagram is

59.	A pinion with radius r1, and inertia I1 is driving a gear with radius r2 and inertia I2. Torque τ1 is applied on pinion. The following are free body diagrams of pinion and gear showing important forces (F1 and F2) of interaction. Which of the following relations hold true?
Answer» A pinion with radius $r_{1},$ and inertia $I_{1}$ is driving a gear with radius $r_{2}$ and inertia $I_{2} .$ Torque $τ_{1}$ is applied on pinion. The following are free body diagrams of pinion and gear showing important forces $(F_{1} a n d F_{2})$ of interaction. Which of the following relations hold true?

60.	A clutch has outer and inner diameter 100 mm and 40 mm respectively. Assuming a uniform pressure of 2 MPa and coefficient of friction of the material is 0.4, the torque carrying capacity of the clutch is
Answer» A clutch has outer and inner diameter $100 m m$ and $40 m m$ respectively. Assuming a uniform pressure of $2 M P a$ and coefficient of friction of the material is $0.4$ , the torque carrying capacity of the clutch is

61.	A uniform ladder 24m long weights 400N It is placed against a vertical wall at an angle of 60∘ with the ground. How far along the ladder can a 1600N man climb before the ladder is on the verge of slipping? The angle of friction at all contact surfaces is 15∘
Answer» A uniform ladder $24 m$ long weights $400 N$ It is placed against a vertical wall at an angle of $60^{\circ}$ with the ground. How far along the ladder can a $1600 N$ man climb before the ladder is on the verge of slipping? The angle of friction at all contact surfaces is $15^{\circ}$

62.	A particle is thrown up vertically with initial velocity 'u'. The velocity-time graph for the motion of the particle considering upward velocity as positive can be represented as
Answer» A particle is thrown up vertically with initial velocity 'u'. The velocity-time graph for the motion of the particle considering upward velocity as positive can be represented as

63.	A mass 35 kg is suspended from a weightless bar AB which is supported by a cable CB and a pin at A as shown in figure. The pin reactions at A on the bar AB are
Answer» A mass 35 kg is suspended from a weightless bar AB which is supported by a cable CB and a pin at A as shown in figure. The pin reactions at A on the bar AB are

64.	An annular disc has a mass m, inner radius R and outer radius 2 R. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is v, the kinetic energy of the disc is
Answer» An annular disc has a mass m, inner radius R and outer radius 2 R. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is v, the kinetic energy of the disc is

65.	In figure, the velocities are in ground frame and the cylinder is performing pure rolling on the plank, velocity of point 'A' would be
Answer» In figure, the velocities are in ground frame and the cylinder is performing pure rolling on the plank, velocity of point 'A' would be