System of Particles and Rotational Motion · Question 46

The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of F = i - j + k acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is .

The center of mass of a thin rectangular plate (fig - x) with sides of length a and b, whose mass per unit area ( ) varies as = 0 xab (where 0 is a constant), would be . [figure]

1. ( 23a, 23b )
2. ( 23a, b2 )
3. ( 13a, b2 )
4. ( a2, b2 )

Two iron solid discs of negligible thickness have radii R1 and R2 and moment of inertia I1 and I2, respectively. For R2 = 2R1, the ratio of I1 and I2 would be 1/x, where x = .

The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the disc and rotating in similar way, is n times higher than the moment of inertia of the given ring. Here, n = . Consider all the bodies have equal masses.

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is

1. 290 g
2. 200 g
3. 190 g
4. 300 g