1.159 Work done in uniform circular motion

Problem 1.159:.A body of mass $‘m’$ is moving in a circle of radius with a constant speed $‘v’$. Calculate the work done by the resultant force in moving the body over half circumference and full circumference respectively. Solution: This is motion along a circular...

1.158 Angular acceleration of a disc

Problem 1.158: The disk has a mass $M$ and a radius $R$. If a block of mass $m$ is attached to the cord, determine the angular acceleration of the disk when the block is released from rest.  Solution: When released, the block falls down vertically due to its weight...

1.157 Force on a rod from a wall

Problem 1.157: A rod of mass $M$ is hinged at one end and is balanced horizontally with the help of a string as shown in the diagram. Determine the force exerted by the wall on the rod.   Solution: The different forces acting on the rod are: weight $Mg$, tension $T$...

1.156 Tension in a string

Problem 1.156: A rod of mass $M$ is hinged at one end and is balanced horizontally with the help of a string as shown in the diagram. Determine the tension in the string.   Solution: The different forces acting on the rod are: weight $Mg$, tensi on $T$ in the string...

1.155 Work done and change in energy

Problem 1.155: A thin rod of mass $M$ and length $L$ is lying on a horizontal surface with one end hinged to the ground. Determine the work done to lift the other end through a distance $\frac{L}{2}$.  Solution: Here work done is equal to the change in gravitational...

1.154 Moment of inertia

Problem 1.154: Four identical discs of mass $M$ and radius $R$ are arranged as shown in the diagram. Determine the moment of inertia of the system about the axis $X-X’$. Solution: Moment of inertia of the system is the sum of moment of inertia of each disc about the...

1.153 Change in velocity in circular motion

Problem 1.153: A particle is executing uniform circular motion along a circular path of radius $R$ with angular speed $\pi\:rad\:s^{-1}$. Determine the magnitude of change in velocity in one second. Solution: In uniform circular motion, speed remains constant but...

1.152 Frictional force on a disc rolling down an inclined plane

Problem 1.152: A disc of mass $M$ and radius $R$ is rolling down an inclined plane of angle $\theta$ as shown in the given diagram. Determine the magnitude of the frictional force.   Solution:  Forces acting on the disc are gravitational force, normal force from the...

1.151 Acceleration on a smooth inclined plane

Problem 1.151: A block of mass $m$ is released at the highest point on a smooth wedge as shown in the diagram. Determine the acceleration of the block.   Solution: When the block is released, it will slide downward. But what makes it do so? It is the effect of...

1.149 Tension in a string

Problem 1.149: A uniform rod of length $L$ and mass $M$ is hung from a mass-less string of length $2L$ as shown in the diagram. The rod is perfectly in the horizontal plane at equilibrium. Find the tension in the string.  Solution: The string and the rod will make a...

1.149 Torque on a pulley

Problem 1.149: A block of mass $0.5\:kg$ is connected to a string that is wound tightly over a pulley of mass $0.25\:kg$ and radius $5\:cm$ as shown in the diagram. What is the angular acceleration of the pulley at instant when the block has acceleration of...

1.148 Acceleration of a block

Problem 1.148: A block of mass $0.5\:kg$ is connected to a string that is wound tightly over a pulley as shown in the diagram. What is the acceleration of the block at instant when the tension in the string is $3N$? Take acceleration due to gravity as $10\:ms^{-2}$....

1.147 Angular speed of a rotating body

Problem 1.147: Two points on a rigid rod are separated by a distance $r$ which is measured along the rod. At an instant the points are moving with velocities $v$ and $3v$ directed perpendicular to the length of the rod. The rod is pivoted at one end. Find the angular...

1.146 Projectile motion

Problem 1.146: A stone is thrown from the top of a tower of height $50\:m$ with a velocity of $30\:m$ per second at an angle of $30^o$ above the horizontal. Determine the time during which the stone will be in air. Solution: First of all, let us closely examine the...

1.145 Acceleration of a cylinder

Problem 1.145: A rope of negligible mass is wound round a solid cylinder of mass $3\: kg$ and radius $40 \:cm$. What is the angular acceleration of the cylinder about its geometrical axis, if the rope is pulled with a force of $30\: N$? Assume that there is no...

1.144 Compression of a spring

Problem 1.144: A massless spring of spring constant $K$ is kept between a block of mass $M$ and a rigid wall as shown. The coefficient of static friction between the block and the floor is $\mu$. Find the maximum compression of the spring. Solution: The spring can be...

1.43 Tension in the string of a simple pendulum

Problem 1.43: A simple pendulum of length $L$ and mass $m$ is oscillating with an amplitude of $\theta$ about a fixed point as shown. Determine the tension in the string when the bob is at the extreme end. Solution: At the extreme point, velocity of the bob is zero....

1.142 Rotational equilibrium

Problem 1.142: A rectangular slab of length $L$ and mass $M$ is kept on a table as shown in the diagram. Determine the maximum length through which the slab can be moved over the edge of the table without toppling? Solution: The slab will topple when there is net...