A mass of 6 kg is suspended by a rope of lengih 2 m form the ceiling . A force of 50 N in the horizonlal direction is applied at the mid Point P of the rope as shown in figure. what is the angle the rope makes. with the vertical in equilibrium ? Neglect mass of the rope:

Two bodies A and B cach of mass are fixed together by a massless spring force acts on the mass B as shown in figure. At the instant shown, a body A has an accelcration a. what is the acceleration of B?

A block of mass m=4 kg is placed over a rough inclined plane as shown in figure, The cocfficient of friction between the block and plane is s=0.6.A force F=10 N is applied on the block of an angle at 30° The contact force between the block and the plane is

If the unit vectors  and  are inclined at an angle  such that , then  lies in the interval

For an interval, square bracket denotes close bracket and parantheses means open bracket. Close bracket means that point is included in the interval. Opem bracket means the point is not included in the interval.

A planet moving along an elliptical orbit is closest to the sun at a distance r_¹ and farthest away at a distance of r₂. If v₁ and v₂ are the liner velocities at these points respectively, then the ratio  is

A block of mass is resting on a rough inclined plane of inclination 30° as shown in fignre. The coefficient of friction between the block and the plane is =0.5. What minimam force shald be applied perpendicular to the plane of block does not slip on the plane ?

Three blocks having equal mass of are hanging on a string passing over a pulley as shown in figure. whal will be the tension prodoced in a string connccting the blocks B and C.

A bag of sand of mass m is suspended hy rope. A bullet of mass m/30 is fired at it with a velocity v and gets embedded into it . The velocity of the bag finally is

Three blocks A,B, and C of equal mass are placed one over the other, one on a smooth horizontal ground as shown in figure. Cefixime of friction between any two blocks of A,B and is 0.5. What would he the maximum value of mass of block D so that the blocks A,B and C move without slipping over each other '?

body of mass m rests on horizontal surface. The coefficient of friction between the body and the surface is if the body is pulled by a force P as shown in figure the limiting function between body and surface will be

A satellite of mass m is orbiting close to the surface of the earth (Radius R=6400 km ) has a K.E. K. The corresponding K.E. of satellite to escape from the earth's gravitational field is

Three masses and are connccied to cach other with threads and are placed on a table as shown in figure. The alcceleration with which the system is moving is

If the surfaces shown in figure are frictionless, the ratio of and is

Three blocks of masers and by massless strings as shown in figure, on a frictionless table. They are Pulled with the force . If and the tension will

Assertion  If  then 

Reason  If   is a homogeneous function in  of degree '  ' then 

For such questions, we should know the formulas related to homogeneous equation. Before solving the equation, we have to see if the given function is a homegenous function. A homegenous function has same degree for all its terms.

Two blocks of Nass and ane connected a heavy string placed on rough horizontal plane, the 4 kg block is Pulled with a constant force F. The co-efficient of friction between the blocks and the ground is , what is the value of F, So that the tension in the spring is constant throughout during the motion of the blocks?