Question 1:If point A is in equilibrium under the action of the applied forces, the values of tensions TAB and TAC are respectively.
[2006]
Explanation

TAB cos 60º = TAC cos 30º ...(i)
TAB sin 60º + TAC sin 30º = 600 ...(ii)
Solving equations (i) and (ii), we get
TAB = 520N and TAC = 300N
Question 2:A weight of 500 N is supported by two metallic ropes as shown in the figure. The values of tensions T1 and T2 are respectively
[2015]
Explanation
Using sine rule


T1 = 500 x sin 120º
T2 = 500 sin 150º
T1 = 433 N, T2 = 250N
Question 3:A car having weight W is moving in the direction as shown in the figure. The center of gravity (CG) of the car is located at height h from the ground, midway between the front and rear wheels. The distance between the front and rear wheels is l. The acceleration of the car is a, and acceleration due to gravity is g. The reaction on the front wheels(Rf) and rear wheels (Rr) are given by:
[2019]
Explanation
8. Here, Reaction on front wheels = Rf Reaction on rear wheels = Rr


Question 4: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
[1997]
Explanation

For block, T2 = mg = 343.35 N ...(i)

∴ T1 = 829.74 N
∑Fy = O
Ry – T2 + T1 sinθ = O
∴ Ry = O
∑Fx = O
Rx – T1 cosθ = O
Rx = 755.4 N
Question 5:A ladder AB of length 5 m and weight (W) 600 N is resting against a wall. Assuming frictionless contact at the floor (B) and the wall (A), the magnitude of the force P (in newton) required to maintain equilibrium of the ladder is_____.
[2014]
Explanation
Taking moments about B
∑MB = 0
⇒ W × 2 = RA × 3

∑H = 0
⇒ RA = P = 400 N
Question 6:A spring scale indicates a tension T in the right hand cable of the pulley system shown in Neglecting the mass of the pulleys and ignoring friction between the cable and pulley the mass m is [1995]
Explanation

∑ FV = 0
4T = mg
or m = 4T/g