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1.

Two like parallel forces P and Q act at the ends of a strianght ruler of length l. What is the distance by which the resultant of the forces will shift along the ruler If P is doubled ?

Answer» Correct Answer - `(PQl)/((P+Q)(2P+Q))`
Discussion
2.

A pulley fixed to the ceiling carries a thread with bodies of masses `m_(1)` and `m_(2)` attached at its ends. The masses of the pulley and thread are negligible, friction is absent. Find the acceleration of the centre of mass`(a_("cm"))` of this system.

Answer» Correct Answer - `a_(cm)=[(m_(1)-m_(2))//(m_(1)+m_(2))]^(2)g`
Discussion
3.

A table has a heavy circular top of radius 1 m and mass 20 kg . It has four light legs of length 1 m fixed symmetrically on its circuference. What is the maximum weight which may be placed anywhere on this table wihtout toppling it?

Answer» Correct Answer - 48.3 kg
Discussion
4.

A particle of mass m is placed upon the smooth face of a prism, also of mass m, which particle is placed , is inclined at an angle `alpha` to the horizontal . Show that when the particle has moved a distance x down the face of the prism the prism itself will have moved a distance of `(1)/(2)x "cos" alpha`

Answer» Correct Answer - N//A
Discussion
5.

A cone of height h and semivertical angle `alpha` is just held in equilibrium against a smooth vertical wall by a string attached to the apex and tied to the wall at the other end. Calcualate the length of the string.

Answer» Correct Answer - `l=hsqrt((1+(16"tan"^(2)alpha)/(9))`
Discussion
6.

A cylindrical vessel of radius 1 m and height 2 m is half filled with water. Find the centre of mass of the system consisting of cylinder and water. The cylinder has mass 10 kg per square metre of it and density of water 1000 kg `m^(-3)`.

Answer» Correct Answer - 0.514 m above the base
Discussion
7.

A man weighting 60 kgis standing at the centre of a flat boat and he is 20 m from the shore. He walks 8 cm on the boat towards the shore and then halts. The boat weights 200 kg How far is the from the shore at the end of this time? [Hints : As the system is free from external force, centre of mass of the system consisting of man and boat must not move.

Answer» Correct Answer - 13.8 m
Discussion
8.

A dump-bell consists of two weights `W_(1)` and `W_(2)(W_(2) gt W_(1))` and is hinged at a point distant `l_(1)` and `l_(2)` from `W_(1)` and `W_(2)` , respectively . Establish the criterion of stable equilibrium for the vertical position of the dump-bell.

Answer» Correct Answer - `W_(2)l_(2) gt W_(1)l_(1)`
Discussion
9.

A jack of pitch 4 mm is worked by a handle of length 50cm .There is friction between the screw and the nut of it. To overcome the frictional force an extra effort of 0.004 times the load has to be applied . Calculate the least force required to raise and lower a load of 500 kg (take `g=10 ms^(-2)`)

Answer» Correct Answer - 26.36 N,13.6 N
Discussion