A wheel of radius 0.4 m can rotate freely about its axis as shown in the figure. A string is wrapped over its rim and a mass of 4 kg is hung. An angular acceleration of 8 rad-s^-2 produced in it due to the torque. Then, moment of inertia of the wheel is (g =10 ms^-2 )

• 2 kg-m²

• 1 kg-m²

• 4 kg-m²

• 8 kg-m²

An object start sliding on a frictionless inclined plane and from same height another object start falling freely.

• both will reach with same speed

• both will reach with same acceleration

• both will reach in same time

• None of the above

Two rigid bodies A and B rotate with rotational kinetic energies E, and E, respectively. The moments of inertia of A and B about the axis of rotation are I_A and I_B respectively.

If ${\mathrm{I}}_{\mathrm{A}} = \frac{{\mathrm{I}}_{\mathrm{B}}}{2}$ and  E_A = 100 = E_B, the ratio of angular momentum (L_A ) of A to the angular  momentum ( L_B ) of B is

• 25

• 5/4

• 5

• 1/4

64.

The working principle of a ball point pen is

• Bernoulli's theorem

• surface tension

• gravity

• viscosity

Progressive waves are represented by the equation y₁ = a sin (ωt - x )  and y₂ = bcos (ωt - x ).  The phase difference wave is

• 0^o

• 45^o

• 90^o

• 180^o

If applied torque on a system is zero, i.e.,Τ = 0 , then for that system

• ω = 0

• α = 0

• J = 0

• F = 0

Match the following

• C- 2, D - 1

• A - 4, B - 3

• A - 3, C -2

• B-2, A - 1

A tangential force acting on the top of sphere of mass m kept on a rough horizontal place as shown in figure

If the sphere rolls without slipping, then the acceleration with which the centre of sphere moves, is

• $\frac{10 \mathrm{F}}{7 \mathrm{m}}$

• $\frac{\mathrm{F}}{2 \mathrm{m}}$

• $\frac{3 \mathrm{F}}{7 \mathrm{m}}$

• $\frac{7 \mathrm{F}}{2 \mathrm{m}}$

A solid sphere is set into motion on a rough horizontal surface with a linear speed v in the forward direction and an angular speed $\frac{\mathrm{v}}{\mathrm{R}}$ in the anticlockwise direction as shown in figure. Find the linear speed of the sphere when it stops rotating and ω = $\frac{\mathrm{v}}{\mathrm{R}}$

• $\frac{3\mathrm{v}}{5}$

• $\frac{2 \mathrm{v}}{5}$

• $\frac{4 \mathrm{v}}{3}$

• $\frac{7 \mathrm{v}}{3}$

Two blocks of masses m₁ and m₂ are connected by a spring of spring constant k. The block of mass m₂ is given a sharp empulse so that it acquires a velocity v₀ towards right. Find the maximum elongation that the spring will suffer.

• ${\left[\frac{{\mathrm{m}}_1 {\mathrm{m}}_2}{{\mathrm{m}}_1 + {\mathrm{m}}_2}\right]}^{\frac{1}{2}}$ v₀

• $\left(\frac{{\mathrm{m}}_1 + {\mathrm{m}}_2}{{\mathrm{m}}_1 - {\mathrm{m}}_2}\right)$v₀

• ${\left[\frac{{\mathrm{m}}_1 + {\mathrm{m}}_2}{{\mathrm{m}}_1 - {\mathrm{m}}_2}\right]}^{\frac{1}{2}}$ v₀ 

• ${\left[\frac{2{\mathrm{m}}_1 + {\mathrm{m}}_2}{{\mathrm{m}}_1 {\mathrm{m}}_2}\right]}^{\frac{1}{2}}$ v₀