A ball is spun with angular acceleration $$\alpha$$ = 6t^{2} $$-$$ 2t where t is in second and $$\alpha$$ is in rads^{$$-$$2}. At t = 0, the ball has angular velocity of 10 rads^{$$-$$1} and angular position of 4 rad. The most appropriate expression for the angular position of the ball is :

A $$\sqrt {34} $$ m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If E_{f} and F_{w} are the reaction forces of the floor and the wall, then ratio of $${F_w}/{F_f}$$ will be :

(Use g = 10 m/s^{2}.)

Match List-I with List-II

List-I | List-II | ||
---|---|---|---|

(A) | Moment of inertia of solid sphere of radius R about any tangent. | (I) | $${5 \over 3}M{R^2}$$ |

(B) | Moment of inertia of hollow sphere of radius (R) about any tangent. | (II) | $${7 \over 5}M{R^2}$$ |

(C) | Moment of inertia of circular ring of radius (R) about its diameter. | (III) | $${1 \over 4}M{R^2}$$ |

(D) | Moment of inertia of circular disc of radius (R) about any diameter. | (IV) | $${1 \over 2}M{R^2}$$ |

Choose the correct answer from the options given below :

One end of a massless spring of spring constant k and natural length l_{0} is fixed while the other end is connected to a small object of mass m lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity $$\omega$$ about an axis passing through fixed end, then the elongation of the spring will be :