Laws of Motion

A horizontal force of 10 N is applied on a block of mass 1.5 kg which is initially at rest on a rough horizontal surface. The work done by the applied force in a time of 6 s from the beginning of the motion is (Acceleration due to gravity $...

A block of mass $\sqrt{2} \mathrm{~kg}$ is placed on a rough horizontal surface. A force ' $F$ ' acting upwards at an angle of $45^{\circ}$ with the horizontal causes the block to start motion. If the coefficient of static friction between ...

A force separately produces accelerations of $18 \mathrm{~ms}^{-2}$, $9 \mathrm{~ms}^{-2}$ and $6 \mathrm{~ms}^{-2}$ in three bodies of masses $P, Q$ and $R$ respectively. If the same force is applied on a body of mass $P+Q+R$, then the acc...

A truck of mass 8 ton is carrying a block of mass 2 ton. If a breaking force of 25 kN is applied on the truck, then the frictional force acting on the block is (Coefficient of static friction between the block and the truck is 0.3 )

A man of mass 60 kg is standing in a lift moving up with a retardation of $2.8 \mathrm{~ms}^{-2}$. The apparent weight of the man is

If the system of blocks shown in the figure is released from rest, the ratio of the tensions $T_1$ and $T_2$ is (Neglect the mass of the string shown in the figure)

A block of mass 5 kg is kept on a smooth horizontal surface. A horizontal stream of water coming out of a pipe of area of cross-section $5 \mathrm{~cm}^{2}$ hits the block with a velocity of $5 \mathrm{~ms}^{-1}$ and rebounds back with the ...

A block is kept on a rough horizontal surface. The acceleration of the block increases from $6 \mathrm{~ms}^{-2}$ to $11 \mathrm{~ms}^{-2}$ when the horizontal force acting on it increases from 20 N to 30 N . The coefficient of kinetic fric...

If a man of mass 50 kg is in a lift moving down with an acceleration equal to acceleration due to gravity, then the apparent weight of the man is

A man weighing 75 kg is standing in a lift. The weight of the man standing on a weighing machine kept in the lift when the lift is moving downwards freely under gravity is

A body of weight 50 N is placed on a horizontal surface as shown in the figure. The minimum force required to move the body is 28.28 N . The frictional force and the normal reaction are respectively

Two blocks of masses $w_1$ and $w_2$ are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up with an acceleration $g$, then the tension in the string will be

A person initially at rest, starts walking towards east without slipping or skidding. What is the type of friction acting on the person from the ground and in which direction the frictional force acts?

A body of mass 6 kg is moving with a uniform velocity $4 \mathrm{~ms}^{-1}$. Its velocity changes to $6 \mathrm{~ms}^{-1}$ when a force of 12 N acts on it. Then its displacement is

At time $t=0$, a force $F=\alpha t$, where $t$ is time in seconds, is applied to a body of mass 1 kg , resting on a smooth horizontal plane. If the direction of the force makes an angle of $45^{\circ}$ with the horizontal, then the velocity...

A motor car moving with velocity $7 \mathrm{~m} / \mathrm{s}$ stops at 10 m distance when brakes are applied. What is the relation between the resistance force $R$ and the weight $w$ of the car? (take, value of $g=9.8 \mathrm{~m} / \mathrm{...

A constant horizontal force $\mathbf{F}$ of magnitude 10 N is applied to a block $A$ and this produces an acceleration of magnitude $20 \mathrm{~m} / \mathrm{s}^2$. If this block $A$ is then kept against another block $B$ of mass 1.5 kg as ...

A time varying force acts on a ball of mass 100 g for 2 ms . The force versus time curve is shown below. If the initial speed of the ball is $10 \mathrm{~m} / \mathrm{s}$, then the speed of ball after 2 ms is

Two blocks of masses 1 kg and 2 kg connected by a light rod and the system is slipping down a rough incline angle $45^{\circ}$ with the horizontal. The frictional coefficient at both the contacts is 0.4 . If the acceleration of the system i...

A block is placed on a parabolic shape ramp given by equation, $y=\frac{x^2}{20}$. If the coefficient of static friction $\left(\mu_s\right)$ is 0.5 , then what is the maximum height above the ground at which the block can be placed without...

A block of mass 4 kg at rest on a rough inclined plane making an angle of $\theta$ with the horizontal. The coefficient of static friction between the block and plane is 0.5 and the frictional force on the block is 14.14 N , find the value ...

A block rests on a fixed wedge inclined at an angle $\theta$. The coefficient of friction between the block and plane is $\mu$. The maximum value of $\theta$ for the block to remain motionless on the
wedge is

A box of mass $m$ is in equilibrium under the application of three forces as shown below. If the magnitude of $\mathbf{F}_1$ is 10 N , what is the magnitude of $\mathbf{F}_3$ ?

The velocity of an object of mass 2 kg is given by $\mathbf{v}=\left(8 t \hat{\mathbf{i}}+3 t^2 \hat{\mathbf{j}}\right) \mathrm{m} / \mathrm{s}$, where $t$ is time in seconds. What will be the direction of net force on the object relative t...

A block of mass $m=2 \mathrm{~kg}$ is initially at rest on a horizontal surface. A horizontal force $\mathbf{F}_1=(6 \mathrm{~N}) \hat{\mathbf{i}}$ and a vertical force $\mathbf{F}_2=(10 \mathrm{~N}) \hat{\mathbf{j}}$ are then applied to th...

An infinite number of masses are placed on a frictionless table and they are connected via massless strings. Their masses follow the sequence, $m, \frac{m}{2}, \frac{m}{6}, \ldots \ldots \ldots . . \frac{m}{n!}, \ldots \ldots$. and they are...

A block is between two surfaces as shown in the figure. Find the normal reaction at both surfaces. [Assume, $g=10 \mathrm{~m} / \mathrm{s}^2$ ]

When a bullet is fired from a rifle its momentum becomes $20 \mathrm{~kg}-\mathrm{ms}^{-1}$. If the velocity of the bullet is $1000 \mathrm{~ms}^{-1}$, then what is its mass?

A block of mass 3 kg is pressed against a vertical wall by applying a force $F$ at an angle $30^{\circ}$ to the horizontal as shown in the figure. As a result, the block is prevented from falling down. If the coefficient of static friction ...