A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 m/s. To give an initial upward acceleration of 20$m/s^{2},$ the amount of gas ejected per second to supply the needed thrust will be (Take g = 10 $m/s^{2}$)
- 127.5 kg/s
- 137.5 kg/s
- 155.5 kg/s
- 187.5 kg/s
The Correct Option is D
Solution and Explanation
Exhaust speed (v) = 800 m/s
Acceleration of rocket (a) = 20 $m/s^{2}$
Gravitational acceleration (g) $=10 m/s^{2}$
We know that upward force
F = m(g +a) = 5000(10+20)
= 5000 x 30 = 150000 N.
We also know that amount of gas ejected
$\left(\frac{d m}{d t}\right)=\frac{F}{V}=\frac{150000}{800}=187.5 $ kg/s
Top Questions on Rotational motion
If $\overrightarrow{\mathrm{L}}$ and $\overrightarrow{\mathrm{P}}$ represent the angular momentum and linear momentum respectively of a particle of mass ' $m$ ' having position vector $\overrightarrow{\mathrm{r}}=\mathrm{a}(\hat{\mathrm{i}} \cos \omega \mathrm{t}+\hat{\mathrm{j}} \sin \omega \mathrm{t})$. The direction of force is
- JEE Main - 2025
- Physics
- Rotational motion
A uniform circular disc of radius \( R \) and mass \( M \) is rotating about an axis perpendicular to its plane and passing through its center. A small circular part of radius \( R/2 \) is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.
- JEE Main - 2025
- Physics
- Rotational motion
Which of the following are correct expression for torque acting on a body?
A. $\ddot{\tau}=\ddot{\mathrm{r}} \times \ddot{\mathrm{L}}$
B. $\ddot{\tau}=\frac{\mathrm{d}}{\mathrm{dt}}(\ddot{\mathrm{r}} \times \ddot{\mathrm{p}})$
C. $\ddot{\tau}=\ddot{\mathrm{r}} \times \frac{\mathrm{d} \dot{\mathrm{p}}}{\mathrm{dt}}$
D. $\ddot{\tau}=\mathrm{I} \dot{\alpha}$
E. $\ddot{\tau}=\ddot{\mathrm{r}} \times \ddot{\mathrm{F}}$
( $\ddot{r}=$ position vector; $\dot{\mathrm{p}}=$ linear momentum; $\ddot{\mathrm{L}}=$ angular momentum; $\ddot{\alpha}=$ angular acceleration; $\mathrm{I}=$ moment of inertia; $\ddot{\mathrm{F}}=$ force; $\mathrm{t}=$ time $)$
Choose the correct answer from the options given below:- JEE Main - 2025
- Physics
- Rotational motion
A wheel of radius $ 0.2 \, \text{m} $ rotates freely about its center when a string that is wrapped over its rim is pulled by a force of $ 10 \, \text{N} $. The established torque produces an angular acceleration of $ 2 \, \text{rad/s}^2 $. Moment of inertia of the wheel is............. kg m².
- JEE Main - 2025
- Physics
- Rotational motion
A tube of length 1m is filled completely with an ideal liquid of mass 2M, and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is \( F \) and the angular velocity of the tube is \( \omega \), then the value of \( \alpha \) is ______ in SI units.
- JEE Main - 2025
- Physics
- Rotational motion
Questions Asked in NEET exam
- With the help of the given pedigree, find out the probability for the birth of a child having no disease and being a carrier (has the disease mutation in one allele of the gene) in the F3 generation.
- NEET (UG) - 2025
- Genetics
- Consider the diameter of a spherical object being measured with the help of a Vernier Callipers. Suppose its 10 Vernier Scale Divisions (V.S.D.) are equal to its 9 Main Scale Divisions (M.S.D.). The least count in the M.S. is 0.1 cm and the zero of V.S. is at -0.1 cm when the jaws of Vernier callipers are closed. If the main scale reading for the diameter is \(M = 5\) cm and the number of coinciding vernier division is 8, the measured diameter after zero error correction, is:
- NEET (UG) - 2025
- Measurement of length
- In some appropriate units, time (t) and position (x) relation of a moving particle is given by \(t = \alpha x^2 + \beta x\). The acceleration of the particle is :
- NEET (UG) - 2025
- Kinematic equations for uniformly accelerated motion
The output (Y) of the given logic implementation is similar to the output of an/a …………. gate.
- NEET (UG) - 2025
- Logic gates
- Two identical point masses P and Q, suspended from two separate massless springs of spring constants \(k_1\) and \(k_2\), respectively, oscillate vertically. If their maximum velocities are the same, the ratio of the amplitude of P to the amplitude of Q is :
- NEET (UG) - 2025
- Waves and Oscillations
Concepts Used:
Rotational Motion
Rotational motion can be defined as the motion of an object around a circular path, in a fixed orbit.
Rotational Motion Examples:
The wheel or rotor of a motor, which appears in rotation motion problems, is a common example of the rotational motion of a rigid body.
Other examples:
- Moving by Bus
- Sailing of Boat
- Dog walking
- A person shaking the plant.
- A stone falls straight at the surface of the earth.
- Movement of a coin over a carrom board
Types of Motion involving Rotation:
- Rotation about a fixed axis (Pure rotation)
- Rotation about an axis of rotation (Combined translational and rotational motion)
- Rotation about an axis in the rotation (rotating axis)