MCQ
The angular velocity of the earth at present in $\omega $ . With what angular velocity should it rotate so that weight of body at the equator appears to be zero ? ....... $\omega $
- A$2$
- B$8$
- ✓$17$
- D$289$
✓
Answer
Correct option: C.
$17$
c
The present value of angular velocity
The present value of angular velocity
$=\frac{2 \pi}{86400}=1.2 \times 10^{-3}$ rad/sec. $A$ body at
equator appears weightless if weight provides centripetal force,
i.e., $m \omega^{2} r=m g$
Or $\omega=\sqrt{\frac{g}{r}}=\sqrt{\frac{9.8}{6.4 \times 10^{6}}}$ rad/sec.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Consider a drop of rain water having mass $1\, g$ falling from a height of $1\, km.$ It hits the ground with a speed of $50\, m s^{-1}$. Take $g$ constant with a value $10 \, m s^{-1}$. The work done by the $(i)$ gravitational force and the $(ii)$ resistive force of air is
→The satellite of mass $m$ revolving in a circular orbit of radius $r$ around the earth has kinetic energy $E$. Then its angular momentum will be
→A solid sphere (mass $2\ M$) and a thin hollow spherical shell (mass $M$) both of the same size, roll down an inclined plane, then
→The equation of a progressive wave is $y = a\,\sin \,\left( {\frac{\pi }{2}x - 200\pi t} \right)$ . The frequency of the wave will be .... $Hz$
→If an ideal gas has volume $V$ at $27°C$ and it is heated at a constant pressure so that its volume becomes $1.5V.$ Then the value of final temperature will be ....... $^oC$
→In the figure, the ball $A$ is released from rest when the spring is at its natural (unstretched) length. For the block $B$ of mass $M$ to leave contact with the ground at some stage, the minimum mass of $A$ must be
→The unit of Planck's constant is
A force of $2\hat i + 3\hat j + 4\hat k\;N$acts on a body for $4$ second, produces a displacement of $(3\hat i + 4\hat j + 5\hat k)m.$The power used is.......$W$
→Block of $1 kg$ is initially in equilibrium and is hanging by two identical springs $A$ and $B$ as shown in figures. If spring $A$ is cut from lower point at $t=0$ then, find acceleration of block in $ms^{^{-2}}$ at $t = 0.$
→A particle of man $2\ kg$ is moving on a circular path of radius $10m$ with a speed of $5ms$ and its speed is increasing at rate of $3\ ms^{-1}.$ Find the force acting on the particle.
→