A ball is spun with angular acceleration $$\alpha$$ = 6t2 $$-$$ 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 Ef and Fw are the reaction forces of the floor and the wall, then ratio of $${F_w}/{F_f}$$ will be :
(Use g = 10 m/s2.)
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 :
When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :