Physics Test - ...

The driver of a train moving with a constant speed v₁  along a straight track sights another train at a distance d ahead of him on the same track moving in the same direction with a constant speed v₂. He at once applies the brakes and gives his train a constant retardation f. There will be a collision of the trains if:

Two particles are projected under gravity with speed 4 m/s and 3 m/s simultaneously from same point and at angles 53° and 37° with the horizontal surface respectively as shown in figure. Then :

A projectile is projected with velocity v such that its range is twice the greatest height attained. Then its range is

If error in measuring diameter of a circle is 4%, the error in circumference of the circle would be

Two stones are thrown vertically upwards simultaneously from the same point on the ground with initial speed u₁=30  m/sec and  u₂=50 m/sec. Which of the curves represent correct variation (for the time interval in which both reach the ground) of relative position (x₂−x₁) and relative velocity (v₂−v₁) of second stone with respect to respect to first with time (t). Assume that stones do not rebound after hitting.

Figure shows a mass M is attached to the middle of a string, the two ends of which are passing over two pulleys  P₁ and P₂. The ends of strings are attached to masses M₁ and M₂. If the two parts of the string attached to M are inclined at an angle 2θ and the instantaneous downward velocity of the masses M₁ and M₂  be v, what is the upward velocity of M ?

Two bodies of different masses ma and mb are dropped from two different heights, a and b respectively. The ratio of times taken by the two bodies to drop through this distance is

Find the height above the surface of the earth where weight of a body becomes half.

A constant force F is applied at the top of a ring as in figure. M is the mass and R is the radius of the ring. The change in angular momentum of particle about point of contact in a time t is.

A particle of mass m is executing uniform circular motion on a path of radius r. If v is the speed and p the magnitude of its linear momentum, then the radial force acting on the particle is:

In the figure shown all the surfaces are smooth. All the blocks A,B and C are movable X-axis is horizontal and y-axis vertical as shown. Just after the system is released from the position as shown:

A body crosses the topmost point of a vertical circle with critical speed. What will be its centripetal acceleration when the string is horizontal:

The potential energy of a particle is given by $U=\frac{a}{r^2}\frac{b}{r}$ where a and b are positive constants, r is the distance from the centre of the field. The stable equilibrium position of the particle corresponds to the distance given by

If the radius of the earth were to shrink by one per cent, its mass remaining the same, the value of g on the earth's sur­face would.

A block of mass M is at rest on a rough horizontal surface. The coefficient of friction between the block and the surface isμ. A force F=Mg acting at an angle θ with the vertical side of the block pulls it. In which of the following cases, the block can be pulled along the surface?