List of practice Questions

A particle is doing simple harmonic motion of amplitude 0.06 m and time period 3.14 s. The maximum velocity of the particle is _______ cm/s.
A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be:
Fig
A block
A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :
A player caught a cricket ball of mass 150 g moving at a speed of 20 m/s. If the catching process is completed in 0.1 s, the magnitude of force exerted by the ball on the hand of the player is:
(31.2) How do emotions and perceptions reflect in this source?
Consider the circuit shown in the figure. The potential difference between points A and B is: \includegraphics[width=0.4\linewidth]{872image.png}
Seema and Laksh were partners in a firm sharing profits and losses in the ratio of 2:1. Their capitals were ₹ 2,00,000 and ₹ 1,80,000 respectively. They admitted Aadi as a new partner on 1\textsuperscript{st April, 2023 for \(\frac{1}{5}\) share in future profits. Aadi brought ₹ 1,50,000 as his share of capital. The goodwill of the firm on Aadi’s admission will be:}
An iron bar of length L has magnetic moment M. It is bent at the middle of its length such that the two arms make an angle 60° with each other. The magnetic moment of this new magnet is :

In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most 95 studied Physics; at least 75 and at most 90 studied Chemistry; 30 studied both Physics and Chemistry; 50 studied both Chemistry and Mathematics; 40 studied both Mathematics and Physics and 10 studied none of these subjects. Let m and n respectively be the least and the most number of students who studied all the three subjects. Then m + n is equal to _____

Sodium atoms emit a spectral line with a wavelength in the yellow, 589.6 nm. What is the difference in energy between the two energy levels involved in the emission of this spectral line?
The speed \( v \) of a wave on a string depends on the tension \( F \) in the string and the mass per unit length \( m/L \) of the string. If it is known that [F] = [ML][T]–2, the values of the constants \( a \) and \( b \) in the following equation for the speed of a wave on a string are: \[ v = (\text{constant}) F^a \left( \frac{m}{L} \right)^b \]
A stone is dropped from the top of a tower. The height through which it falls in the first 3 seconds of its motion equals the height through which it falls in the last second of its motion. To reach the ground, the stone takes time equal to (g = 10 m/s\(^2\)):
A particle executes SHM with a period of 6 s and amplitude of 3 cm. Its maximum speed in cm/s is:
A body of mass \( m \) moves along the X-axis such that at time \( t \), its position is \( x(t) = \alpha t^4 - \beta t^3 + \gamma t \), where \( \alpha \), \( \beta \), and \( \gamma \) are constants. The acceleration of the body is:
A 7 kg object is subjected to two forces, \( F_1 = 20i + 30j \, \text{N} \) and \( F_2 = 8i - 50j \, \text{N} \). Find the acceleration of the object.

The motion of a particle in the XY plane is given by \( x(t) = 25 + 6t^2 \, \text{m} \); \( y(t) = -50 - 20t + 8t^2 \, \text{m} \). The magnitude of the initial velocity of the particle, \( v_0 \), is given by:

Rain, pouring down at an angle \( \alpha \) with the vertical, has a constant speed of 10 m/s. A woman runs against the rain with a speed of 8 m/s and sees that the rain makes an angle \( \beta \) with the vertical. The relation between \( \alpha \) and \( \beta \) is given by:
A car goes around a curve of radius 48 m. If the road is banked at an angle of 15° with the horizontal, the maximum speed in kilometers per hour at which the car can travel if there is to be no tendency to skid even on very slippery pavement (tan 15° = 0.27 approximately) is:
An electrical appliance is rated 1500 W, 250 V. This appliance is connected to a 250 V supply mains. The current drawn by the appliance (assuming unity power factor) is:
Two identical coins of mass 8 g are 50 cm apart on a tabletop. How many times larger is the weight of one coin than the gravitational attraction of the other coin for it? (G = \( 6.67 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \), g = 9.81 m/s\(^2\)):
A straight rod of length \( L \) extends from \( x = a \) to \( x = L + a \). Find the gravitational force it exerts on a point mass \( m \) at \( x = 0 \) if the mass per unit length of the rod is \( \mu = A + Bx^2 \):
A block falls from a table 0.6 m high. It lands on an ideal, mass-less, vertical spring with a force constant of 2.4 kN/m. The spring is initially 25 cm high, but it is compressed to a minimum height of 10 cm before the block is stopped. Find the mass of the block (g = 9.81 m/s\(^2\)):
An engine pumps water continuously through a hose. If the speed with which the water passes through the hose nozzle is \( v \), and if \( k \) is the mass per unit length of the water jet as it leaves the nozzle, what is the rate at which kinetic energy is being imparted to the water?
n identical light bulbs, each designed to draw power \( P \) from a certain voltage supply are joined in series across that supply. The total power which they will draw is:
One mole of an ideal gas is at temperature \( T \) K. The \( \gamma \) value of this gas is \( \frac{5}{3} \). Now the gas does 12R Joules of work adiabatically (R is the universal gas constant). Then the final temperature of the gas will be: