A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg , kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(A) \(3.5 \mathrm{~m} / \mathrm{s}^2\)

Step-by-step Solution

Detailed explanation

Torque about bottom point
\(\begin{aligned}
& \mathrm{F} \times 2 \mathrm{r}=\mathrm{I} \alpha \\
& 49 \times 2 \mathrm{r}=\frac{7}{5} \mathrm{mr}^2 \alpha \\
& 14=4 \mathrm{r} \alpha
\end{aligned}\)
As sphere rolls without slipping
\(\begin{aligned}
& \mathrm{a}=\mathrm{r} \alpha \\
& \mathrm{a}=\frac{14}{4}=\frac{7}{2}=3.5 \mathrm{~m} / \mathrm{s}^2
\end{aligned}\)

Same subject

A Carnot engine with efficiency \(50\,\%\) takes heat from a source at \(600\,K\). In order to increase the efficiency to \(70\,\%\), keeping the temperature of sink same, the new temperature of the source will be \(.........\,K\)

JEE Mains 2023 Medium
An electron in a hydrogen atom revolves around its nucleus with a speed of \(6.76 \times 10^6\,ms ^{-1}\) in an orbit of radius \(0.52\,\mathring A\). The magnetic field produced at the nucleus of the hydrogen atom is \(......T\).

JEE Mains 2023 Medium
The maximum velocity of the photoelectrons emitted from the surface is \(v\) when light of frequency \(n\) falls on a metal surface. If the incident frequency is increased to \(3n\) , the maximum velocity of the ejected photoelectrons will be

JEE Mains 2017 Medium
A rectangles solid box of length \(0.3\, m\) is held horizontally, with one of its sides on the edge of a platform of height \(5\,m\). When released, it slips off the table in a very short time \(= 0.01\, s\), remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to:

JEE Mains 2019 Hard
Three masses \(m_1 = 4\) kg, \(m_2 = 4\) kg and \(m_3 = 6\) kg are suspended from a fixed smooth frictionless pulley as shown in the figure below. The value of \(T_1/T_2\) is _____.
(take \(g = 10\) m/s\(^2\))

JEE Mains 2026 Hard
In an experiment to find \(emf\) of a cell using potentiometer, the length of null point for a cell of emf \(1.5\,V\) is found to be \(60\,cm\). If this cell is replaced by another cell of \(emf\; E\). the length-of null point increases by \(40\,cm\). The value of \(E\) is \(\frac{x}{10} V\). The value of \(x\) is \(............\)

JEE Mains 2023 Medium

Explore more questions on app

From JEE Mains

The equation \(\lambda=\frac{1.227}{ x } nm\) can be used to find the de-Brogli wavelength of an electron. In this equation \(x\) stands for : Where,\(m =\) mass of electron \(P =\) momentum of electron \(K =\) Kinetic energy of electron \(V =\) Accelerating potential in volts for electron

JEE Mains 2022 Easy
A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from its centre. The radius of gyration about this axis is \(\sqrt{n}\) cm. The value of n is

JEE Mains 2026 Easy
The time dependence of the position of a particle of mass \(m = 2\) is given by \(\vec r\,(t)\, = \,2t\,\hat i\, - 3{t^2}\hat j\) Its angular momentum with respect to the origin at time \(t = 2\) is

JEE Mains 2019 Hard
Two capacitors, each having capacitance \(40\,\mu F\) are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant \(K\) such that the equivalence capacitance of the system became \(24\,\mu F\). The value of \(K\) will be.

JEE Mains 2022 Medium
Identify the logic operation performed by the given circuit.

JEE Mains 2024 Hard
The width of one of the two slits in a Young's double slit experiment is three times the other slit. If the amplitude of the light coming from a slit is proportional to the slit-width, the ratio of minimum to maximum intensity in the interference pattern is \(x: 4\) where \(x\) is ..... .

JEE Mains 2021 Hard

Explore more questions on app