Laws of Motion ...

At time $$t$$ second, a particle of mass $$3\ kg$$ has position vector $$\vec {r}$$ metre where $$\vec {r} = 3t\hat {i} - 4\cos t \hat {j}$$. The impulse of the force during the time interval $$0 < t < \dfrac {\pi}{2}$$ is

A $$0.1\ kg$$ body moves at a constant speed of $$10\ m/s$$. It is pushed by applying a constant force for $$2\sec$$. Due to this force, it starts moving exactly in the opposite direction with a speed of $$4\ m/s$$. Then

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If a number of forces act on a body and the body is in static of dynamic equilibrium then

A ring of mass $$5\ kg$$ sliding on a frictionless vertical rod is connected by a block $$B$$ of mass $$10\ kg$$ by the help of a massless string. Then at the equilibrium of the system the value of $$\theta$$ is

In the figure, a block of weight $$60\ N$$ is placed on a rough surface. The coefficient of friction between the block and the surfaces is $$0.5$$. What minimum can be the weight $$W$$ such that the block does not slip on the surface?

A system of two blocks A and B are connected to an inextensible massless string as shown in Fig. The pulley is massless and frictionless. Initially, the system is at rest. A bullet of mass 'm' moving with a velocity 'u' as shown hits block 'B' and gets embedded into it. The impulse imparted by tension force to the block of mass $$3m$$ is?

Consider the situation shown in the figure. The wall is smooth but the surfaces of $$A$$ and $$B$$ in contact are rough. Then

In the given figure, pulleys and strings are massless. For equilibrium of the system, the value of $$\alpha$$ is

Consider the system as shown. The wall is smooth, but the surface of block A & B in contact is rough. the friction force on B due to A is equilibrium is: