LMOI-02-MOMENT OF INERTIA- CONTINUOUS OBJECTS-PART 1 -VIKAS SIR

Let f:[0,2]->R be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1 L e t :F(x)=int_0^(x^2)f(sqrt(t))dtforx in [0,2]dotIfF^(prime)(x)=f^(prime)(x) . for all x in (0,2), then F(2) equals (a) e^2-1 (b) e^4-1 (c) e-1 (d) e^4

The thin semi-circular part ABC has mass m_1 and diameter AOC has mass m_2 Here , axis passes through mid-point of diameter and the axis is perpendicular to plane ABC . Here , AO = OC = R. The moment of inertia of this Composite system about the axis is

For a uniform sphere a small cavity is formed as shown STATEMENT-1 : Moment of inertia of the sphere about AA is greater than moment of inertia about BB' . and STATEMENT-2 : Mass removed was more closer to the axis AA.

Statement - 1 : Let I_(1) and I_(2) be the moment of inertia of two bodies of identical geometrical shapes, the first made of aluminium and second of iron then I_(1) lt I_(2) . Becaause Statement - 2 : Moment of inertia does not depends on shape

Two bodies with moment of inertia I_1 and I_2 (I_1 gt I_2) have equal angular momenta. If their kinetic energy of rotation are E_1 and E_2 respectively, then.

A solid cylinder of mass 20kg has length 1 m and radius 0.2 m. Then its moment of inertia (in kg- m^(2) ) about its geometrical axis is :

Show that moment of inertia of a solid body of any shape changes with temperature as I=I_0(1+2 alphatheta). Where I_0 is the moment of inertia at 0^@C and alpha is the coefficient of linear expansion of the solid.

Match the following: Moment of inertia of body (in kgm^(2) ) (shown in column - 1) about the axis (shown in column - 2)

ABC is a plane lamina of the shape of an equilateral triangle. D , E are mid points of AB,AC and G is the centroid of the lamina . Moment of inertia of the lamina about an axis passing through G and perpendicular to the plane ABC is I_0 If part ADE is removed, the moment of inertia of a remaining part about the same axis is (NI_0)/16 where N is an integer . Value of N is

Moment of inertia of a solid about its geometrical axis is given by 1 =2/5 MR^(2) where M is mass & R is radius. Find out the rate by which its moment of inertia is changing keeping dnsity constant at the moment R= 1 m , M=1 kg & rate of change of radius w.r.t. time 2 ms^(-1)