Fairer pay for women must be backed up by stronger policies at work, according to Facebook's Sheryl Sandberg.

But the firm's chief operating officer, in an interview for BBC Radio 4's Desert Island Discs, said the first step is to "start paying women well".

She chose Beyonce's empowering Run The World (Girls) as her first song.

She said: "We start telling little girls not to lead at a really young age and we start to tell boys [to] lead at a very young age. That is a mistake."

"I believe everyone has inside them the ability to lead and we should let people choose that not based on their gender but on who they are and who they want to be."

In an emotional interview, Ms Sandberg also spoke of the sudden death of her husband in 2015 and the effect on her two young children.

"I didn't know anyone could cry this much," she said.

Ms Sandberg made headlines in 2013 with her book "Lean in" about female empowerment in the workplace.

It became a worldwide bestseller, but was criticised by some for being elitist and unrealistic for many women not in her privileged position.

'We need policy'

In the interview, she also called for more to be done around the gender pay gap between men and women.

Ms Sandberg admitted she had struggled with self-doubt at Harvard and recognised that women more than men underestimated their own worth, preventing them from putting themselves forward or asking for a pay rise.

"We need to start paying women well and we need the public and the corporate policy to get there," she said.

"Certainly, women applying for jobs at the same rate as men, women running for office at the same rate as men, that has got to be part of the answer."

'I'm sadder'

Following the sudden death of her husband Dave Goldberg, Ms Sandberg described herself a "different" person now.

She found him on the floor of a gym with a head injury after he had suffered a heart attack whilst they were on a weekend away.

Sometimes tearful, she said: "I'm sadder. I didn't know anyone could cry this much. I asked my sister - she is a doctor - and she said the majority of your body is water," she joked.

Media playback is unsupported on your device Media caption 'I felt like I had stepped into a void, like I could barely breathe' - Sheryl Sandberg

She chose One by U2 as the record she would keep if the other seven were washed away because Mr Goldberg had loved the band, adding that music had been incredibly important to them both - her husband was the founder of online music site, Launch Media.

Another of her eight tracks was Queen's You're My Best Friend in tribute to her group of close female friends whom she said helped support her through the ordeal.

Work was 'a lifeline'

Since his death, Ms Sandberg said she had become more empathetic and, at Facebook, doubled the amount of time Facebook employees can take off when an immediate family member dies to 20 days.

She said it was also important to support people and build their confidence if they wanted to come into work.

"I offer people time off, I say can we take that project off you, but when they want to be at work, let them.

"Sometimes for me, the memories of Dave are everywhere, but they are worse at home by far, so for me getting out of the house and having something else to do that was a lifeline.

"I have heard that from many people who have lost a spouse and children."

She said it was impossible to look ahead 10 years, but she wanted her husband's legacy to be one of "life, hope and joy".

'Complicated conversations'

When asked about her meeting with the Home Secretary Amber Rudd to discuss what Facebook was doing to fight terrorism, she said they were "aligned" in their aims.

"Complicated conversations" with governments about encrypted messages on WhatsApp, the social messaging platform that Facebook owns, were also continuing, she said.

Following the Westminster terror attack on 22 March, Ms Rudd wanted the police to have access to encrypted WhatsApp messages that suspects had sent each other.

Ms Sandberg's chosen book was the science fantasy novel "A Wrinkle in Time" written by American writer Madeleine L'Engle, because she said it was a triumph of "light against darkness," and her luxury was a journal.

You can listen to Desert Island Discs on BBC Radio 4 at 11:15 BST on Sunday 30 July and afterwards on the BBC iPlayer