Overview

A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a < R) by applying a force F at its centre 'O' perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of F required is:

Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial speed. The angle between the initial velocities of the two bodies (in degree) is

An insect is at the bottom of a hemispherical ditch of radius 1 m. It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then h is: (g = 10 ms?²)

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate dm(t)/dt$$ =bv^2(t), where v(t)$$ its instantaneous velocity. The instantaneous acceleration of the satellite is:

Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force $F$ at $a$ point $b$ above its centre of mass (see figure). If the coefficient of friction is $\mu =0.4$ , the maximum possible value of $100*\frac{b}{a}$  for box not to topple before moving i

A mass of $10\mathrm{k}\mathrm{g}$ is suspended by a rope of length $4\mathrm{m}$ , from the ceiling. A force $F$ is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of ${45}^{?}$ with the vertical. Then $\mathrm{F}$ equals: (Take $\mathrm{g}=10{\mathrm{m}\mathrm{s}}^{-2}$  and the rope to be massless)

Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure. A vertical force $\stackrel{?}{P}$  of magnitude 100N is applied at point A of the frame. Suppose the force is $\stackrel{?}{P}$   resolved parallel to the arms AB and AC of the frame. The magnitude of the resolved component along the arm AC is xN. The value of x, to the nearest integer, is------------. [Given : sin(35° ) = 0.573, cos(35° )= 0.819 sin(110° )= 0.939, cos(110° )= -0.342 ]

A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle θ as shown in figure. The coefficient of kinetic is μ_k . Then, the block's acceleration 'a' is given by :

(g is acceleration due to gravity)

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2m and 2m respectively. A moves towards B with a speed of 9m/s and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. All motions occur along same straight line. The final speed of C is:

A force F = (40î + 10?)N acts on a body of mass 5 kg. If the body starts from rest, its position vector r at time t = 10s, will be :