Laws of Motion

Three blocks of masses $m_1=2 \mathrm{~kg}, m_2=3 \mathrm{~kg}$ and $m_3=5 \mathrm{~kg}$ are placed on a horizontal frictionless surface and a force of 30 N pulls the system as shown below．The value of tension $T$ will be

Two spheres $S_1$ and $S_2$ of masses $m_1$ and $m_2$ respectively collide with each other. Initially $S_1$ is at rest and $S_2$ is moving with velocity $v$ along $x$-axis. After collision $S_2$ has a velocity $\frac{v}{2}$ in a direction p...

A force $\vec{F}=a \hat{i}+b \hat{j}+c \hat{k}$ is acting on a body of mass $m$. The body was initially at rest at the origin. The co-ordinates of the body after time ' $t$ ' will be

The minimum force required to start pushing a body up a rough (having co-efficient of friction $\mu$ ) inclined plane is $\vec{F}_1$ while the minimum force needed to prevent it from sliding is $\overrightarrow{F_2}$. If the inclined plane ...

What force \(\mathrm{F}\) is required to start moving this \(10 \mathrm{~kg}\) block shown in the figure if it acts at an angle of \(60^{\circ}\) as shown? \((\mu_s=0.6)\)

A body of mass 2 kg moves in a horizontal circular path of radius 5 m. At an instant, its speed is 2\(\sqrt5\) m/s and is increasing at the rate of 3 m/s\(^2\). The magnitude of force acting on the body at that instant is,

A golf ball of mass 50 gm placed on a tee, is struck by a golf-club. The speed of the golf ball as it leaves the tee is 100 m/s, the time of contact on the ball is 0.02 s. If the force decreases to zero linearly with time, then the force at...

If a string, suspended from the ceiling is given a downward force F1, its length becomes L1. Its length is L2, if the downward force is F2. What is its actual length?

Three blocks are pushed with a force F across a frictionless table as shown in figure above. Let N1 be the contact force between the left two blocks and N2 be the contact force between the right two blocks. Then,

A block of mass m rests on a horizontal table with a coefficient of static friction \(\mu\). What minimum force must be applied on the block to drag it on the table?

Two weights of the mass m1 and m2 (> m1) are joined by an inextensible string of negligible mass passing over a fixed frictionless pulley. The magnitude of the acceleration of the loads is

The velocity (v) of a particle (under a force F) depends on its distance (x) from the origin (with x > 0) \(v \propto {1 \over {\sqrt x }}\). Find how the magnitude of the force (F) on the particle depends on x?

A block of mass m2 is placed on a horizontal table and another block of mass m1 is placed on top of it. An increasing horizontal force F = at is exerted on the upper block but the lower block never moves as a result. If the coefficient of f...

A block of mass 1 kg starts from rest at x = 0 and moves along the X-axis under the action of a force F = kt, where t is time and k = 1 Ns\(-\)1. The distance the block will travel in 6 seconds is

A mass of 1 kg is suspended by means of a thread. The system is (i) lifted up with an acceleration of 4.9 ms\(-\)2. (ii) lowered with an acceleration of 4.9 ms\(-\)2. The ratio of tension in the first and second case is

A bullet emerges from a barrel of length 1.2 m with a speed of 640 ms\(-\)1. Assuming constant acceleration, the approximate time that it spends in the barrel after the gun is fired is

A rocket of mass 100 kg burns 0.1 kg of fuel per sec. If the velocity of exhaust gas is 1 km/sec, then it lifts with an acceleration of

Force required to move a mass of 1 kg at rest on a horizontal rough plane (\(\mu\) = 0.1 and g = 9.8 m/s2) is

A shell of mass 10 kg is moving with a velocity of 10 ms\(-\)1 when it blasts and forms two parts of mass 9 kg and 1 kg respectively. If the 1st mass is stationary, the velocity of the 2nd is